State True or False for the following statements

If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, then (A × B) ∪ (A × C)

= {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}.

The given statement is true.

Explanation:

Now

Cartesian product of set A = {1, 2, 3} and B = {3, 4} is

A×B = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}

Cartesian product of set A = {1, 2, 3} and C = {4, 5, 6} is

A×C = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}

Now,

(A×B)∪(A×C) is union of set A×B and set A×C elements, so

(A×B)∪(A×C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}

This is the required Cartesian product.