Question

If A = {x : x = 6n, n ∈ W and n < 6}, B = {x : x = 2n, n ∈ N and 2 < n ≤ 9} and C = {x : x = 3n+2, n ∈ N and 4 ≤ n < 10}

Answer 1

Answer:

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).Read more on Sarthaks.com - https://www.sarthaks.com/960088/if-a-x-x-6-n-w-and-n-6-b-x-x-2n-n-n-and-2-n-9-and-c-x-x-3n-n-n-and-4-n-10