Ordered Pairs in set

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 $(a,b)$, where $a$ is called the first element and $b$ is the second element.

Key Points

• Unlike sets, the order of elements in an ordered pair is important.
• Two ordered pairs $(a,b)$ and $(c,d)$ are equal if and only if $a=c$ and $b=d$.
• Ordered pairs are used to define relations and functions in mathematics.

Examples

1. Consider the ordered pair $(2,5)$. Here, 2 is the first element and 5 is the second element. 2. The ordered pair $(3,7)$ is not the same as $(7,3)$, because the order of elements is different. 3. If $A=\{1,2\}$ and $B=\{3,4\}$, then the ordered pair $(1,3)$ is different from $(3,1)$.

Usage

Ordered pairs are used in coordinate geometry to represent points on the plane, such as $(x,y)$, where $x$ is the horizontal coordinate and $y$ is the vertical coordinate.