Editing Complement of a Set (section)

== Examples of Complement of a Set ==

=== Example 1: Numbers ===  
Let the universal set be:

<math>U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}</math>

and let

<math>A = \{2, 4, 6, 8, 10\}</math>

Step 1: Universal set <math>U</math> contains numbers 1 to 10.  
Step 2: Set <math>A</math> contains even numbers 2, 4, 6, 8, 10.  
Step 3: Elements in <math>U</math> but not in <math>A</math> are odd numbers: 1, 3, 5, 7, 9.  
Step 4: Complement of <math>A</math> is:

<math>A' = \{1, 3, 5, 7, 9\}</math>

=== Example 2: Letters ===  
Let

<math>U = \{\text{a}, \text{b}, \text{c}, \text{d}, \text{e}\}</math>

and

<math>B = \{\text{a}, \text{c}, \text{e}\}</math>

Then,

<math>B' = \{\text{b}, \text{d}\}</math>

since these are the letters in <math>U</math> not in <math>B</math>.

=== Example 3: Shapes ===  
Consider a universal set of shapes:

<math>U = \{\text{circle}, \text{square}, \text{triangle}, \text{rectangle}\}</math>

and set

<math>C = \{\text{circle}, \text{triangle}\}</math>

The complement of <math>C</math> is:

<math>C' = \{\text{square}, \text{rectangle}\}</math>

=== Example 4: Numbers Between 1 and 15 ===  
Let

<math>U = \{1, 2, 3, \dots, 15\}</math>

and

<math>D = \{5, 6, 7, 8, 9\}</math>

The complement of <math>D</math> is all numbers from 1 to 15 except 5 through 9:

<math>D' = \{1, 2, 3, 4, 10, 11, 12, 13, 14, 15\}</math>

=== Example 5: Prime Numbers Up to 20 ===  
Let

<math>U = \{1, 2, 3, \dots, 20\}</math>

and

<math>E = \{2, 3, 5, 7, 11, 13, 17, 19\}</math>  (the prime numbers)

Then the complement of <math>E</math> is all numbers from 1 to 20 that are not prime:

<math>E' = \{1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20\}</math>