What is Ordered Pair?

In short

An ordered pair $(a, b)$ is two objects written in a fixed order. The pair $(1, 2)$ is different from $(2, 1)$ .

In simple words

In an ordinary set $\{1, 2\}$ and $\{2, 1\}$ are the same set, but order matters in an ordered pair. The first element is the first coordinate, and the second is the second. Two ordered pairs are equal only when both coordinates match. A point on a graph is an ordered pair $(x, y)$ . The Cartesian product $A \times B$ is the set of all ordered pairs with the first element from $A$ and the second from $B$ .

Example

If $A = \{1, 2\}$ and $B = \{a, b\}$ , then $A \times B = \{(1, a), (1, b), (2, a), (2, b)\}$ , which has $2 \times 2 = 4$ ordered pairs.

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