Chapter 1: Sets

Q1. If U = {1,2,3,4,5,6,7,8,9,10} and A = {2,4,6,8,10}, find A'.

Solution

A' = U - A = {1, 3, 5, 7, 9}

Q2. Let A = {1,2,3}, B = {3,4,5}. Find A union B, A intersection B.

Solution

A ∪ B = {1,2,3,4,5}
A ∩ B = {3}

Q3. Verify De Morgan's law for A = {1,2,3,4} and B = {3,4,5,6} with U = {1,...,8}.

Solution

(A ∪ B)' = {1,2,5,6,7,8}' = {7,8}
A' ∩ B' = {5,6,7,8} ∩ {1,2,7,8} = {7,8}
Both are equal. ✓

Q4. In a class of 50 students, 30 take Maths, 25 take Physics, 10 take both. How many take neither?

Solution

n(M ∪ P) = 30 + 25 - 10 = 45
Neither = 50 - 45 = 5