In Mathematics, we come across many corresponding relations of one property with another (e.g number m is less than number n, line l is parallel to line m, set A is a subset of set B etc.). These pairs of objects may be linked establishing relations between them.

Cartesian Products of Sets

The cartesian product P × Q of two non-empty sets P and Q, is the set of all ordered pairs of elements from P and Q, i.e.,

For example, non empty sets P (Red, Blue) and Q (a,b,c). Then P × Q would be (Red, a), (Red, b), (Red, c), (Blue,a), (Blue,b), (Blue,c)

Properties of Ordered Pairs

Two ordered pairs are equal, if and only if the corresponding first elements are equal and the second elements are also equal.

If there are p elements in A and q elements in B, then there will be pq elements in A × B, i.e., if n(A) = p and n(B) = q, then n(A × B) = pq.