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05:5905:59, 10 June 2025 Bias-Variance Tradeoff (hist | edit) [2,658 bytes] Thakshashila (talk | contribs) (Created page with "= Bias-Variance Tradeoff = '''Bias-Variance Tradeoff''' is a fundamental concept in machine learning that describes the balance between two sources of error that affect model performance: bias and variance. == What is Bias? == Bias refers to the error introduced by approximating a real-world problem, which may be complex, by a simpler model. A model with high bias pays little attention to the training data and oversimplifies the problem. * High bias can cause '''unde...")
05:5805:58, 10 June 2025 Regularization (hist | edit) [2,440 bytes] Thakshashila (talk | contribs) (Created page with "= Regularization = '''Regularization''' is a technique in machine learning used to prevent '''overfitting''' by adding extra constraints or penalties to a model during training. == Why Regularization is Important == Overfitting happens when a model learns noise and details from the training data, harming its ability to generalize on new data. Regularization discourages overly complex models by penalizing large or unnecessary model parameters. == Common Types of Regul...")
05:5605:56, 10 June 2025 Train-Test Split (hist | edit) [2,316 bytes] Thakshashila (talk | contribs) (Created page with "= Train-Test Split = '''Train-Test Split''' is a fundamental technique in machine learning used to evaluate the performance of a model by dividing the dataset into two parts: a training set and a testing set. == What is Train-Test Split? == The dataset is split into: * '''Training Set:''' Used to train the machine learning model. * '''Testing Set:''' Used to evaluate how well the trained model performs on unseen data. This helps measure the model’s ability to ge...")
05:5305:53, 10 June 2025 Underfitting (hist | edit) [1,937 bytes] Thakshashila (talk | contribs) (Created page with "= Underfitting = '''Underfitting''' occurs when a machine learning model is too simple to capture the underlying pattern in the data, resulting in poor performance on both training and unseen data. == What is Underfitting? == Underfitting means the model fails to learn enough from the training data. It shows high errors during training and testing because it cannot capture important trends. == Causes of Underfitting == * '''Model Too Simple:''' Using a linear model...")
05:5105:51, 10 June 2025 Overfitting (hist | edit) [2,515 bytes] Thakshashila (talk | contribs) (Created page with "= Overfitting = '''Overfitting''' is a common problem in machine learning where a model learns the training data too well, including its noise and outliers, resulting in poor performance on new, unseen data. == What is Overfitting? == When a model is overfitted, it captures not only the underlying pattern but also the random fluctuations or noise in the training dataset. This causes the model to perform excellently on training data but badly on test or real-world data...")
05:4605:46, 10 June 2025 Evaluation Metrics (hist | edit) [3,123 bytes] Thakshashila (talk | contribs) (Created page with "= Evaluation Metrics = '''Evaluation Metrics''' are quantitative measures used to assess the performance of machine learning models. Choosing the right metric is essential for understanding how well a model performs, especially in classification and regression problems. == Why Are Evaluation Metrics Important? == * Provide objective criteria to compare different models. * Help detect issues like overfitting or underfitting. * Guide model improvement and selection. * R...")
05:4505:45, 10 June 2025 Cost-Sensitive Learning (hist | edit) [2,729 bytes] Thakshashila (talk | contribs) (Created page with "= Cost-Sensitive Learning = '''Cost-Sensitive Learning''' is a machine learning approach that incorporates different costs for different types of classification errors, helping models make better decisions in situations where misclassification errors have unequal consequences. == Why Cost-Sensitive Learning? == In many real-world problems, different mistakes have different costs. For example: * In medical diagnosis, a false negative (missing a disease) may be more co...")
05:4405:44, 10 June 2025 Area Under Precision-Recall Curve (AUPRC) (hist | edit) [2,331 bytes] Thakshashila (talk | contribs) (Created page with "= Area Under Precision-Recall Curve (AUPRC) = The '''Area Under the Precision-Recall Curve''' ('''AUPRC''') is a single scalar value that summarizes the performance of a binary classification model by measuring the area under its Precision-Recall (PR) curve. == What is the Precision-Recall Curve? == The Precision-Recall Curve plots: * '''Precision''' (y-axis): the proportion of true positive predictions among all positive predictions. * '''Recall''' (x-axis): the pro...")
05:4005:40, 10 June 2025 Imbalanced Data (hist | edit) [2,634 bytes] Thakshashila (talk | contribs) (Created page with "= Imbalanced Data = '''Imbalanced Data''' refers to datasets where the classes are not represented equally. In classification problems, one class (usually the positive or minority class) has far fewer examples than the other class (negative or majority class). == Why is Imbalanced Data a Problem? == Machine learning models often assume that classes are balanced and try to maximize overall accuracy. When data is imbalanced, models tend to be biased toward the majority...")
05:3605:36, 10 June 2025 Cross Validation (hist | edit) [2,746 bytes] Thakshashila (talk | contribs) (Created page with "= Cross-Validation = '''Cross-Validation''' is a statistical method used to estimate the performance of machine learning models on unseen data. It helps ensure that the model generalizes well and reduces the risk of overfitting. == Why Cross-Validation? == When training a model, it is important to test how well it performs on data it has never seen before. Simply evaluating a model on the same data it was trained on can lead to overly optimistic results. Cross-validat...")
05:3505:35, 10 June 2025 Model Selection (hist | edit) [3,186 bytes] Thakshashila (talk | contribs) (Created page with "= Model Selection = '''Model Selection''' is the process of choosing the best machine learning model from a set of candidate models based on their performance on a given task. It is a critical step to ensure the selected model generalizes well to new, unseen data. == Why Model Selection is Important == Different algorithms and model configurations may perform differently depending on the dataset and problem. Selecting the right model helps: * Improve prediction accur...")
05:3405:34, 10 June 2025 Threshold Tuning (hist | edit) [2,652 bytes] Thakshashila (talk | contribs) (Created page with "= Threshold Tuning = '''Threshold Tuning''' is the process of selecting the best decision threshold in a classification model to optimize performance metrics such as Precision, Recall, F1 Score, or Accuracy. It is crucial in models that output '''probabilities''' rather than direct class labels. == Why Threshold Tuning Matters == Many classifiers (e.g., Logistic Regression, Neural Networks) output a probability score indicating how likely an instance b...")
05:3305:33, 10 June 2025 AUC Score (hist | edit) [2,689 bytes] Thakshashila (talk | contribs) (Created page with "= AUC Score (Area Under the Curve) = The '''AUC Score''' refers to the '''Area Under the Curve''' and is a popular metric used to evaluate the performance of classification models, especially in binary classification tasks. Most commonly, AUC represents the area under the ROC Curve (Receiver Operating Characteristic Curve) or under the Precision-Recall Curve (PR Curve). == What is AUC? == AUC measures the ability of a model to distinguish between positive and...")
05:3205:32, 10 June 2025 Precision-Recall Curve (hist | edit) [3,086 bytes] Thakshashila (talk | contribs) (Created page with "= Precision-Recall Curve = The '''Precision-Recall Curve''' (PR Curve) is a graphical representation used to evaluate the performance of binary classification models, especially on '''imbalanced datasets''' where the positive class is rare. It plots '''Precision''' (y-axis) against '''Recall''' (x-axis) for different classification thresholds. == Why Use Precision-Recall Curve? == In many real-world problems like fraud detection, disease diagnosis, or spam filtering,...")
05:3005:30, 10 June 2025 Model Evaluation Metrics (hist | edit) [3,410 bytes] Thakshashila (talk | contribs) (Created page with "= Model Evaluation Metrics = '''Model Evaluation Metrics''' are quantitative measures used to assess how well a machine learning model performs. They help determine the accuracy, reliability, and usefulness of models in solving real-world problems. == Importance of Evaluation Metrics == Without evaluation metrics, it's impossible to know whether a model is effective or not. Metrics guide model selection, tuning, and deployment by measuring: * Accuracy of predictions...")
05:2905:29, 10 June 2025 Classification (hist | edit) [3,130 bytes] Thakshashila (talk | contribs) (Created page with "= Classification = '''Classification''' is a fundamental task in '''machine learning''' and '''data science''' where the goal is to predict discrete labels (categories) for given input data. It is a type of '''supervised learning''' since the model learns from labeled examples. == What is Classification? == In classification, a model is trained on a dataset with input features and known target classes. Once trained, the model can assign class labels to new, unseen dat...")
05:2705:27, 10 June 2025 ROC Curve (hist | edit) [2,678 bytes] Thakshashila (talk | contribs) (Created page with "= ROC Curve = The '''ROC Curve''' ('''Receiver Operating Characteristic Curve''') is a graphical tool used to evaluate the performance of binary classification models. It plots the '''True Positive Rate (TPR)''' against the '''False Positive Rate (FPR)''' at various threshold settings. == Purpose == The ROC Curve shows the trade-off between sensitivity (recall) and specificity. It helps assess how well a classifier can distinguish between two classes. == Definitions...")
05:2605:26, 10 June 2025 Micro F1 Score (hist | edit) [2,700 bytes] Thakshashila (talk | contribs) (Created page with "= Micro F1 Score = The '''Micro F1 Score''' is an evaluation metric used primarily in '''multi-class''' and '''multi-label classification''' tasks. Unlike Macro F1 Score, it calculates global counts of true positives, false positives, and false negatives across all classes, then uses these to compute a single Precision, Recall, and F1 Score. It is most useful when the dataset is '''imbalanced''' and you care more about overall performance than per-class fai...")
05:2505:25, 10 June 2025 Weighted F1 (hist | edit) [2,730 bytes] Thakshashila (talk | contribs) (Created page with "= Weighted F1 Score = The '''Weighted F1 Score''' is a metric used in multi-class classification to evaluate model performance by computing the F1 Score for each class and taking the average, weighted by the number of true instances for each class (i.e., the class "support"). It is especially useful when working with '''imbalanced datasets''', where some classes are more frequent than others. == Definition == :<math> \text{Weighted F1} = \sum_{i=1}^{C} w_i \cdot F1_i...")
05:2405:24, 10 June 2025 Macro F1 (hist | edit) [2,412 bytes] Thakshashila (talk | contribs) (Created page with "= Macro F1 Score = The '''Macro F1 Score''' is an evaluation metric used in multi-class classification tasks. It calculates the F1 Score independently for each class and then takes the average (unweighted) across all classes. Unlike the regular F1 Score, which is typically applied to binary classification, the Macro F1 is designed for problems involving more than two classes. == Definition == 1. Compute Precision and Recall for each class individually 2. Compute...")
05:2305:23, 10 June 2025 Complementary metrics (hist | edit) [3,031 bytes] Thakshashila (talk | contribs) (Created page with "= Complementary Metrics in Machine Learning = '''Complementary Metrics''' refer to pairs or groups of evaluation metrics that together provide a more complete and balanced understanding of a classification model’s performance. Because no single metric is perfect, especially in real-world and imbalanced datasets, these metrics are used together to highlight different strengths and weaknesses of a model. == Why Use Complementary Metrics? == Using only one metric like...")
05:2205:22, 10 June 2025 F1 Score (hist | edit) [2,460 bytes] Thakshashila (talk | contribs) (Created page with "= F1 Score = The '''F1 Score''' is a performance metric used in classification problems that balances the trade-off between Precision and Recall (also known as Sensitivity). It is especially useful when the dataset is imbalanced, and both false positives and false negatives are important. == Definition == The F1 Score is the '''harmonic mean''' of Precision and Recall. :<math> F1 = 2 \cdot \frac{\text{Precision} \cdot \text{Recall}}{\text{Precision} + \te...")
05:2105:21, 10 June 2025 Specificity (hist | edit) [2,494 bytes] Thakshashila (talk | contribs) (Created page with "= Specificity = '''Specificity''', also known as the '''True Negative Rate (TNR)''', is a performance metric in binary classification tasks. It measures the proportion of actual negative instances that are correctly identified by the model. == Definition == :<math> \text{Specificity} = \frac{TN}{TN + FP} </math> Where: * '''TN''' = True Negatives – actual negatives correctly predicted * '''FP''' = False Positives – actual negatives incorrectly predicted as positi...")
05:2005:20, 10 June 2025 Sensitivity (hist | edit) [2,293 bytes] Thakshashila (talk | contribs) (Created page with "= Sensitivity = '''Sensitivity''', also known as '''Recall''' or the '''True Positive Rate (TPR)''', is a performance metric used in classification problems. It measures how well a model can identify actual positive instances. == Definition == :<math> \text{Sensitivity} = \frac{TP}{TP + FN} </math> Where: * '''TP''' = True Positives – actual positives correctly predicted * '''FN''' = False Negatives – actual positives incorrectly predicted as negative Sensitivit...")
05:2005:20, 10 June 2025 Accuracy (hist | edit) [2,110 bytes] Thakshashila (talk | contribs) (Created page with "= Accuracy = '''Accuracy''' is one of the most commonly used metrics to evaluate the performance of a classification model in machine learning. It tells us the proportion of total predictions that were correct. == Definition == :<math> \text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN} </math> Where: * '''TP''' = True Positives * '''TN''' = True Negatives * '''FP''' = False Positives * '''FN''' = False Negatives Accuracy answers the question: '''"Out of all predict...")
05:1805:18, 10 June 2025 Recall (hist | edit) [1,738 bytes] Thakshashila (talk | contribs) (Created page with "= Recall = '''Recall''' is a metric used in classification to measure how many of the actual positive instances were correctly identified by the model. It is also known as '''sensitivity''' or the '''true positive rate'''. == Definition == :<math> \text{Recall} = \frac{TP}{TP + FN} </math> Where: * '''TP''' = True Positives – correctly predicted positive instances * '''FN''' = False Negatives – actual positives incorrectly predicted as negative Recall answers th...")
05:1805:18, 10 June 2025 Precision (hist | edit) [1,617 bytes] Thakshashila (talk | contribs) (Created page with "= Precision = '''Precision''' is a metric used in classification tasks to measure how many of the predicted positive results are actually correct. It is also known as the '''positive predictive value'''. == Definition == :<math> \text{Precision} = \frac{TP}{TP + FP} </math> Where: * '''TP''' = True Positives – correct positive predictions * '''FP''' = False Positives – incorrect positive predictions Precision helps to answer the question: '''"Of all the items la...")
05:1305:13, 10 June 2025 Confusion Matrix (hist | edit) [2,740 bytes] Thakshashila (talk | contribs) (Created page with "= Confusion Matrix = '''Confusion Matrix''' is a performance measurement tool used in machine learning, particularly for classification problems. It provides a summary of prediction results on a classification problem by comparing the actual labels with those predicted by the model. == What is a Confusion Matrix? == A confusion matrix is a table that describes the performance of a classification model. It shows how many instances were correctly or incorrectly predicte...")

04:2204:22, 5 June 2025 Neural Network (hist | edit) [3,999 bytes] Thakshashila (talk | contribs) (Created page with "= Neural Network = '''Neural Networks''' are a class of algorithms within Machine Learning and Deep Learning that are designed to recognize patterns. They are inspired by the structure and function of the biological brain and are used to approximate complex functions by learning from data. == Overview == A neural network consists of interconnected units (called '''neurons''' or '''nodes''') organized in layers. These layers process input data through weighted c...")
04:2104:21, 5 June 2025 Data Science (hist | edit) [3,648 bytes] Thakshashila (talk | contribs) (Created page with "= Data Science = '''Data Science''' is an interdisciplinary field that uses scientific methods, algorithms, and systems to extract knowledge and insights from structured and unstructured data. It integrates techniques from statistics, computer science, and domain-specific knowledge to turn raw data into actionable intelligence. == Overview == Data Science combines aspects of data analysis, machine learning, data engineering, and software development to address complex...")
04:2004:20, 5 June 2025 Deep Learning (hist | edit) [3,701 bytes] Thakshashila (talk | contribs) (Created page with "= Deep Learning = '''Deep Learning''' is a subfield of Machine Learning concerned with algorithms inspired by the structure and function of the brain, known as artificial neural networks. It is at the heart of many recent advances in Artificial Intelligence. == Overview == Deep learning models automatically learn representations of data through multiple layers of abstraction. These models excel at recognizing patterns in unstructured data such as images, audio,...")
04:2004:20, 5 June 2025 Artificial Intelligence (hist | edit) [3,871 bytes] Thakshashila (talk | contribs) (Created page with "= Artificial Intelligence = '''Artificial Intelligence (AI)''' is a branch of computer science that aims to create systems or machines that exhibit behavior typically requiring human intelligence. These behaviors include learning, reasoning, problem-solving, perception, language understanding, and decision-making. == Overview == Artificial Intelligence involves the design and development of algorithms that allow computers and software to perform tasks that would normal...")
04:1804:18, 5 June 2025 What is Machine Learning (hist | edit) [2,772 bytes] Thakshashila (talk | contribs) (Created page with "= What is Machine Learning = '''Machine Learning (ML)''' is a subfield of artificial intelligence (AI) that focuses on the development of systems that can learn from data and improve their performance over time without being explicitly programmed. == Overview == Machine Learning allows computers to recognize patterns, make decisions, and predict outcomes based on historical data. It contrasts with traditional programming, where rules and logic are manually coded. == T...")

04:5404:54, 24 May 2025 Problem: Find (A ∩ B) × (B ∩ C) (hist | edit) [1,102 bytes] Thakshashila (talk | contribs) (Created page with "= Problem: Find (A ∩ B) × (B ∩ C) = Given sets: <math>A = \{3, 5, 7\}</math> <math>B = \{7, 8\}</math> <math>C = \{8, 9\}</math> == Step 1: Find the Intersection A ∩ B == Intersection means elements common to both sets. Elements of A: 3, 5, 7 Elements of B: 7, 8 Common element is: <math>A \cap B = \{7\}</math> == Step 2: Find the Intersection B ∩ C == Elements of B: 7, 8 Elements of C: 8, 9 Common element is: <math>B \cap C = \{8\}</mat...")
04:4704:47, 24 May 2025 Ahmed Zewail (hist | edit) [2,182 bytes] Thakshashila (talk | contribs) (Created page with "= Ahmed Zewail - The Father of Femtochemistry = '''Ahmed Hassan Zewail''' (1946–2016) was an Egyptian-American scientist known as the Father of Femtochemistry. He won the '''Nobel Prize in Chemistry''' in 1999 for his pioneering work on observing chemical reactions at extremely fast timescales. == Early Life and Education == * Born in Damanhur, Egypt, in 1946 * Studied at Alexandria University in Egypt * Completed his PhD at the University of Pennsylvania, USA...")
04:4604:46, 24 May 2025 Antoine Lavoisier (hist | edit) [2,397 bytes] Thakshashila (talk | contribs) (Created page with "= Antoine Lavoisier - The Father of Modern Chemistry = '''Antoine Laurent Lavoisier''' (1743–1794) was a French chemist who is widely regarded as the Father of Modern Chemistry. He revolutionized chemistry by introducing a scientific and quantitative approach to studying matter and chemical reactions. == Early Life and Education == * Born in Paris, France, in 1743 * Educated in science and law, but devoted his life to chemistry * Known for using careful measurem...")
04:4404:44, 24 May 2025 Marie Curie (hist | edit) [2,428 bytes] Thakshashila (talk | contribs) (Created page with "= Marie Curie - The Pioneer of Radioactivity = '''Marie Curie''' (1867–1934) was a world-renowned scientist known for her groundbreaking work on '''radioactivity'''. She was the first woman to win a Nobel Prize, and the only person to win Nobel Prizes in two different scientific fields — Physics and Chemistry. == Early Life and Education == * Born as '''Maria Sklodowska''' in Warsaw, Poland (1867) * Moved to Paris to study at the University of Paris (Sorbonne)...")
04:2404:24, 24 May 2025 Cartesian Product (hist | edit) [2,633 bytes] Thakshashila (talk | contribs) (Created page with "= Cartesian Product - Definition, Explanation, and Examples = The '''Cartesian Product''' is an operation used in mathematics to combine two sets and form a new set made of ordered pairs. This concept is widely used in set theory, coordinate geometry, and computer science. == Definition == If <math>A</math> and <math>B</math> are two sets, the '''Cartesian product''' of <math>A</math> and <math>B</math> is the set of all ordered pairs where: - The first element is fr...")
04:2204:22, 24 May 2025 Cartesian Product of Two Sets (hist | edit) [2,387 bytes] Thakshashila (talk | contribs) (Created page with "= Cartesian Product of Two Sets - Definition and Step-by-Step Examples = The [[Cartesian Product]] of two sets is the set of all possible '''ordered pairs''' where the first element comes from the first set and the second element comes from the second set. == Definition == If <math>A</math> and <math>B</math> are two sets, then the Cartesian Product of <math>A</math> and <math>B</math>, denoted by <math>A \times B</math>, is defined as: <math> A \times B...")
04:1804:18, 24 May 2025 Ordered Pairs in set (hist | edit) [1,290 bytes] Thakshashila (talk | contribs) (Created page with "= Ordered Pairs - Definition and Examples = An '''ordered pair''' is a fundamental concept in mathematics used to represent two elements together with an order that matters. It is usually written as <math>(a, b)</math>, where <math>a</math> is called the '''first element''' and <math>b</math> is the '''second element'''. == Key Points == * Unlike sets, the order of elements in an ordered pair is important. * Two ordered pairs <math>(a, b)</math> and <math>(c, d)</ma...")
04:1604:16, 24 May 2025 De Morgan (hist | edit) [1,458 bytes] Thakshashila (talk | contribs) (Created page with "= Augustus De Morgan - Mathematician Behind De Morgan's Laws = '''Augustus De Morgan''' (1806–1871) was a British mathematician and logician known for his pioneering work in formalizing logic and mathematics. He is famous for formulating the laws that bear his name, called De Morgan's Laws, which are fundamental in set theory, logic, and computer science. == Early Life and Education == - Born in India in 1806, De Morgan moved to England at a young age. - H...")
04:1504:15, 24 May 2025 De Morgan’s Laws (hist | edit) [2,352 bytes] Thakshashila (talk | contribs) (Created page with "= De Morgan's Laws - Definition, Explanation, and Examples = '''De Morgan''''s laws are fundamental rules in set theory that describe the relationship between union, intersection, and complements of sets. They help simplify complex set expressions, especially involving complements. == Statements of De Morgan's Laws == Let <math>A</math> and <math>B</math> be two sets and <math>U</math> be the universal set. 1. The complement of the union of two sets is equal to t...")
04:0704:07, 24 May 2025 Distributive Law of Sets (hist | edit) [2,665 bytes] Thakshashila (talk | contribs) (Created page with "= Distributive Law of Sets - Definition, Explanation, and Examples = The '''distributive law''' shows how union and intersection operations distribute over each other. It is a key property in set theory that helps simplify expressions involving both operations. == Distributive Law of Intersection over Union == For any three sets <math>A</math>, <math>B</math>, and <math>C</math>: <math> A \cap (B \cup C) = (A \cap B) \cup (A \cap C) </math> This means the intersecti...")
03:5503:55, 24 May 2025 Associative Law of Sets (hist | edit) [2,423 bytes] Thakshashila (talk | contribs) (Created page with "= Associative Law of Sets - Definition, Explanation, and Examples = The '''associative law''' is a fundamental property of set operations which states that when performing the same operation multiple times, the grouping (or association) of sets does not affect the result. == Associative Law for Union == For any three sets <math>A</math>, <math>B</math>, and <math>C</math>: <math> (A \cup B) \cup C = A \cup (B \cup C) </math> This means that whether you first unite <...")
03:4703:47, 24 May 2025 Commutative law on sets (hist | edit) [1,666 bytes] Thakshashila (talk | contribs) (Created page with "= Commutative Law of Sets - Definition, Explanation, and Examples = The '''commutative law''' is an important property of some set operations, meaning the order in which we perform the operation does not affect the result. == Commutative Law for Union == For any two sets <math>A</math> and <math>B</math>, the union operation is commutative. This means: <math> A \cup B = B \cup A </math> In words, combining set <math>A</math> with set <math>B</math> is the same as co...")
03:4603:46, 24 May 2025 Complement of a Set (hist | edit) [3,299 bytes] Thakshashila (talk | contribs) (Created page with "= Complement of a Set - Definition, Explanation, and Examples = The '''complement''' of a set contains all elements that are not in the set but belong to a larger, universal set. It helps identify what is "outside" a given set within a specified context. == Definition of Complement == Let <math>U</math> be the universal set, which contains all elements under consideration. The complement of a set <math>A</math>, denoted by <math>A'</math> or <math>\overline{A}</math>,...")
03:4503:45, 24 May 2025 Difference of Sets (hist | edit) [2,523 bytes] Thakshashila (talk | contribs) (Created page with "= Difference of Sets - Definition, Explanation, and Examples = The '''difference''' of two sets is an operation that finds elements that belong to one set but not the other. It is also called the '''relative complement'''. == Definition of Difference == The difference of sets <math>A</math> and <math>B</math>, denoted by <math>A - B</math>, is the set of all elements that are in <math>A</math> but not in <math>B</math>. Mathematically: <math>A - B = \{ x : x \in A \...")
03:4403:44, 24 May 2025 Intersection of Sets (hist | edit) [2,287 bytes] Thakshashila (talk | contribs) (Created page with "= Intersection of Sets - Definition, Explanation, and Examples = The '''intersection''' of two sets is an important set operation that finds all elements common to both sets. == Definition of Intersection == The intersection of two sets <math>A</math> and <math>B</math> is the set containing all elements that are in both <math>A</math> and <math>B</math>. It is denoted by: <math>A \cap B</math> Mathematically: <math>A \cap B = \{ x : x \in A \text{ and } x \in B \}...")
03:4303:43, 24 May 2025 Union of Sets (hist | edit) [2,662 bytes] Thakshashila (talk | contribs) (Created page with "= Union of Sets - Definition, Explanation, and Examples = The '''union''' of two sets is a fundamental operation in set theory. It combines all the elements from both sets into one set without repeating any element. == Definition of Union == The union of two sets <math>A</math> and <math>B</math> is the set containing all elements that belong to either <math>A</math>, or <math>B</math>, or both. It is denoted by: <math>A \cup B</math> Mathematically: <math>A \cup B...")
03:4203:42, 24 May 2025 Operations on sets (hist | edit) [1,772 bytes] Thakshashila (talk | contribs) (Created page with "= Operations on Sets - Overview and Basic Definitions = '''Operations on sets''' are procedures that combine or modify sets to form new sets. They are fundamental in set theory and are widely used in mathematics, computer science, and logic. == Basic Set Operations == Here are the most common operations on sets with brief explanations: * '''Union (∪)''': The union of two sets <math>A</math> and <math>B</math> is the set of all elements that are in <math>A</math> or...")

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