A = {x : x = 6n, n ∈ W, n < 6}
x = 6n
n = {0, 1, 2, 3, 4, 5}
⇒ x = 6 x 0 = 0
x = 6 x 1= 6
x = 6 x 2 = 12
x = 6 x 3 = 18
x = 6 x 4 = 24
x = 6 x 5 = 30
∴ A = {0, 6, 12, 18, 24, 30}
B = {x : x = 2n, n ∈ N, 2 < n ≤ 9}
n = {3, 4, 5, 6, 7, 8, 9}
x = 2n
⇒ x = 2 x 3 = 6
2 x 4 = 8
2 x 5 = 10
2 x 6 = 12
2 x 7 = 14
2 x 8 = 16
2 x 9 = 18
∴ B = {6, 8, 10, 12, 14, 16, 18}
C = {x : x = 3n, n ∈ N, 4 ≤ n < 10}
N = {4, 5, 6, 7, 8, 9}
x = 3 x 4 = 12
⇒ x = 3 x 5 = 15
x = 3 x 6 = 18
x = 3 x 7 = 21
x = 3 x 8 = 24
x = 3 x 9 = 27
x = 2 x 9 = 18
∴ C = {12, 15, 18, 21, 24, 27}
A – (B ∩ C) = (A – B) ∪ (A – C)
L.H.S = R.H.S
B ∩ C = {12,18}
A – (B ∩ C) = {0, 6, 12, 18, 24, 30} – {12, 18} = {0, 6, 24, 30} … (1)
(A – B) = {0, 24, 30}
(A – C) = {0, 6, 30}
(A – B) ∪ (A – C) = {0, 6, 24, 30} … (2)
From (1) and (2), it is verified that
A – (B ∩ C) = (A – B) ∪ (A – C).