Question

A and B are any two non-empty sets and A is proper subset of B. If n(A) = 5, then the minimum possible value of n(A ∆ B) is ____________.

Answer 1

Given A ∩ B = ϕ
A ⊆ B and n(A) = 5
Then minimum possible value of n(A ∆ B)
Since A ⊊ B i.e n(A) ⊊ n(B)
⇒ A ⋃ B = B
A ∩ B =A
n(A ∆ B) = n(A ⋃ B) – n(A ∩ B)

= n(B) – n(A)
= n(B) – 5

i.e n(A ∆ B) = – n(B) – 5 > n(A) – 5 = 0
i.e. n(A ∆ B) > 0
Minimum possible value of n(A ∆ B) = 1