Question

If = {1,2,3}, find the elements (, ) of the Cartesian Product × . State the subset with

the property < .​

Answer 1

Answer:

If A and B are two non-empty sets, then their Cartesian product A × B is the set of all ordered pair of elements from A and B.

A × B = {(x, y) : x ∈ A, y ∈ B}

Suppose, if A and B are two non-empty sets, then the Cartesian product of two sets, A and set B is the set of all ordered pairs (a, b) such that a ∈A and b∈B which is denoted as A × B.

For Example;

1. If A = {7, 8} and B = {2, 4, 6}, find A × B.

Solution:

A × B = {(7, 2); (7, 4); (7, 6); (8, 2); (8, 4); (8, 6)}

The 6 ordered pairs thus formed can represent the position of points in a plane, if a and B are subsets of a set of real numbers.

2. If A × B = {(p, x); (p, y); (q, x); (q, y)}, find A and B.

Solution:

A is a set of all first entries in ordered pairs in A × B.

B is a set of all second entries in ordered pairs in A × B.

Thus A = {p, q} and B = {x, y}

3. If A and B are two sets, and A × B consists of 6 elements: If three elements of A × B are (2, 5) (3, 7) (4, 7) find A × B.