Question

For all sets A, B and C 

Is (A ∩ B) ∪ C = A ∩ (B ∪ C)? Justify your statement.

Answer 1

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)