Ordered pairs and Cartesian products

An ordered pair is a pair of entries in the specific order. The two entries are separated by comma and enclosed within brackets. An ordered pair is a pair of entries in the specific order. The two entries are separated by comma and enclosed within brackets.

For example, if A and B are two non-empty sets, an ordered pair of elements are denoted by (a, b) where aÎA and  bÎB. 'a' is called the first entry or first component and 'b' is called the second entry or second component.

Equality of two ordered pairs (a,b) and (c,d)

(a, b) = (c, d), if a=c and b=d

Note:

Cartesian product of two sets

Let A and B be two non-empty sets, then the cartesian product of A and B denoted by

                                                 A x B = {(a, b) | aÎA, bÎB}.

Example:

A = {1,2,3}

B = {a,b}

A x B = {(1,a), (1,b), (2,a), (2,b), (3,a), (3,b)}

B x A = {(a,1), (a,2),(a,3),(b,1),(b,2),(b,3)}

Note:

If A has m elements, B has n elements, then A x B has mn elements.

(a,b) = (c,d)

a = c and b = d (Equality of ordered pairs).

'a' is called the first entry or first component and 'b' is called the second entry or second component.