Question

Which of the following is correct?

(a) n (A ∪ B) = n (A) + n (B) + n (A ∩ B)

(b) n (A ∪ B) = n (A) – n (B) – n (A ∩ B)

(c) n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

(d) n (A ∩ B) = n (A) + n (B) + n (A ∪ B)

I had been asked this question during an internship interview.

This key question is from Practical Problems on Union and Intersection of Two Sets topic in section Sets of Mathematics – Class 11

Answer 1

Right answer is (c) n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

For explanation I would say: In the Venn diagram,

n (A ∪ B) = a + b + c

n(A) = a + c, n(B) = b + c and n (A ∩ B) = c

n (A) + n (B) – n (A ∩ B) = (a + c) + (b + c)-c = a + b + c.

Hence, n (A ∪ B) = n (A) + n (B) – n (A ∩ B).