Question

If A = {x ∈ W : 5 < x < 10}, B = {3, 4, 5, 6, 7} and C = {x = 2n; n ∈ N and n ≤4}. Find:

A ∩ (B ∪ C)

Answer 1

A = {x ∈ W : 5 < x < 10}
 = {6, 7, 8, 9}
B = {3, 4, 5, 6, 7}
C = {x = 2n; n ∈ N and n ≤4}
x = 2n

When n = 1,
x = 2 x 1
= 2
When n = 2,
x = 2 x 2 
= 4
When n = 3,
x = 2 x 3
= 6
When n =4,
x = 2 x 4
= 8
∴ C = {2, 4, 6, 8}

B ∪ C
= {3, 4, 5, 6, 7} ∪ {2, 4. 6, 8}
= {2, 3, 4, 5, 6, 7, 8}

A ∩ (B ∪ C) 
= {6. 7, 8, 9} ∩ {2, 3, 4, 5, 6, 7, 8}
⇒ A ∩ (B ∪ C) = {6, 7, 8}