Class 11 Applied Maths | Sets and Relations | Holidays Homework 2025

Q1. Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}.

Find A′, B′, A′ ∩ B′, A ∪ B and hence show that ( A ∪ B )′ = A′ ∩ B′.

Answer: 

i. A′ = U − A = {1,4,5,6}

ii. B' = U − B = {1, 2, 6}

iii. A′ ∩ B′ = {1, 6}

iv. A ∪ B = {2, 3, 4, 5}

v. (A ∪ B)′ = U − (A∪B) = {1,6} 

⇒ ( A ∪ B )′ = A′ ∩ B′ (De Morgan's Law)