Question

If U = {x : x ∈ N, x ≤ 10}, A = {2, 3, 4, 8, 10} and B = {1, 2, 5, 8, 10}, then verify that n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

Answer 1

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {2, 3, 4, 8, 10}, B = {1, 2, 5, 8, 10}

n(U) = 10, n(A) = 5, n(B) = 5

(A ∪ B) = {2, 3, 4, 8, 10} ∪ {1, 2, 5, 8, 10}

= {1, 2, 3, 4, 5, 8, 10}

∴ n(A ∪ B) = 7  ...(1)

(A ∩ B) = {2, 3, 4, 8, 10} ∩ {1, 2, 5, 8, 10}

= {2, 8, 10}

n(A ∩ B) = 3

n(A) + n(B) – n(A∩B) = 5 + 5 – 3

= 10 – 3

= 7 ...(2)

From (1) and (2) we get,

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)