Question

Let A = {x ∈ W | x < 2},
B = {x ∈ N | 1 < 1 < × <_
4} and
C = {3,5}. Verify that:
(ii) A × (B ∩ C) = (A × B) ∩ (A × C)
(iii) (A ∪ B) × C = (A × C) ∪ ​

Answer 1

Answer:

LHS = A x (B ∪ C) B ∪ C = {2, 3, 4} ∪ {3, 5} = {2, 3, 4, 5} A x (B ∪ C) = {(0, 2), (0, 3), (0,4), (0, 5), (1, 2) , (1, 3), (1, 4),(1, 5)} … (1) RHS = (A x B) ∪ (A x C) (A x B) = {(0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4)} (A x C) = {(0, 3), (0, 5), (1, 3), (1, 5)} (A x B) ∪ (A x C) = {(0, 2), (0, 3), (0,4), (1, 2), (1, 3), (1, 4), (0, 5), (1, 5)} … (2) (1) = (2), LHS = RHS Hence it is provedRead more on Sarthaks.com - https://www.sarthaks.com/932437/let-a-x-w-x-2-b-x-n-1-x-4-and-c-3-5-verify-that-i-a-x-b-c-a-x-b-a-x-c