Question

For all sets A , B C , is (A∩B)∪C=A∩(B∪C)? Justify your answer.

Answer 1

Step-by-step explanation:

No. consider the following sets A, B and C : A = {1, 2, 3} B = {2, 3, 5} C = {4, 5, 6} Now (A ∩ B) ∪ C = ({1, 2, 3} ∩ {2, 3, 5}) ∪ {4, 5, 6} = {2, 3} ∪ {4, 5, 6} = {2, 3, 4, 5, 6} And A ∩ (B ∪ C) = {1, 2, 3} ∩ [{2, 3, 5} ∪ {4, 5, 6} = {1, 2, 3} ∩ {2, 3, 4, 5, 6} = {2, 3} Therefore, (A ∩ B) ∪ C ≠ A ∩ (B ∪ C)Read more on Sarthaks.com - https://www.sarthaks.com/112391/for-all-sets-a-b-and-c-is-a-b-c-a-b-c-justify-your-statement