Question

If A = {x: x ∈ N, x ≤ 5}, B = {x: x is prime, x < 6} and C = {x: x ∈ N, x is odd and x < 9}. Find (A ∪ B) ∩ (A ∪ C) ?
1. {1, 3, 5, 7, 9 }
2. {1, 2, 3, 4, 5}
3. { 2, 3, 5, 7 }
4. {1, 2, 3, 4, 5, 6, 7, 8}

Answer 1

Correct Answer - Option 2 : {1, 2, 3, 4, 5}

Concept:

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Calculation:

Given: A = {x: x ∈ N, x ≤ 5}, B = {x: x is prime, x < 6} and C = {x: x ∈ N, x is odd and x < 9}

⇒ A = {1, 2, 3, 4, 5}, B = {2, 3, 5} and C = {1, 3, 5, 7}

As we know that, A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Here, we have to find the value of (A ∪ B) ∩ (A ∪ C)

i.e we have to find the value of A ∪ (B ∩ C)

⇒ B ∩ C = {2, 3, 5} ∩ {1, 3, 5, 7} = {3, 5}

⇒ A ∪ (B ∩ C) = {1, 2, 3, 4, 5} ∪ {3, 5} = A

Hence, (A ∪ B) ∩ (A ∪ C) = {1, 2, 3, 4, 5}