Question

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

Answer 1

For all set A, B and C, 

(A ∩ B) ∪ C = A ∩ (B ∩ C) is not true For example 

Let A = {1, 2}, B = {2,3} and C = {3, 4} 

∴ (A ∩ B) ∪ C = ({1,2}) ∩ ({2,3}) ∪ {3, 4} 

= {2,3,4} 

and A ∩ (B ∩ C) = {1,2} ∩ ({2,3} ∪ {3, 4}) 

= {1, 2} ∩ {2,3,4} 

= {2} 

Hence, (A ∩ B) ∪ C ≠ A ∩ (B ∩ C)