If A = {1, 2}, B = {2, 3) and C = {3, 4), then what is cardinality of  (A × B) ∩ (A × C)?

If A = {1, 2}, B = {2, 3) and C = {3, 4), then what is cardinality of  (A × B) ∩ (A × C)? Correct Answer 2

Concept:

The cardinality of a set is a measure of a set's size, meaning the number of elements in the set.

Let, A = {a, b}  and B = {1, 2} then A × B = {(a, 1), (a, 2), (b, 1), (b, 2)}

Calculation:

Here, A = {1, 2}, B = {2, 3) and C = {3, 4)

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

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

(A × B) ∩ (A × C) = {(1, 3), (2, 3)}

∴ Number of elements = Cardinality = 2

Hence, option (3) is correct.