Relations and Functions
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.