If A and B are two sets such that n(A) = 27, n(B) = 35 and n(A ∪ B) = 50, find n(A ∩ B).

Question

Question

This question was previously asked in

Bihar STET Paper I: Mathematics (Held In 2019 - Shift 1)

Answer 1

Given:

n(A) = 27 (number of elements in set A)

n(B) = 35 (number of elements in set B)

n(A ∪ B) = 50 (number of elements in the union of sets A and B)

Concept used:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B) (Inclusion-Exclusion Principle for Sets)

Calculation:

Using the Inclusion-Exclusion Principle:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

⇒ 50 = 27 + 35 - n(A ∩ B)

⇒ 50 = 62 - n(A ∩ B)

⇒ -12 = -n(A ∩ B)

⇒ n(A ∩ B) = 12

∴ The number of elements in the intersection of sets A and B (n(A ∩ B)) is 12.