Q7 of 162 Page 1

For any two sets, prove that:
A ∩ (A ∪ B) = A

= (A ∩ A) ∪ (A ∩ B) [∵intersection is distributive over union]

= A ∪ (A ∩ B) [∵ A ∩ A = A]

= A.

For three sets A, B, and C, show that

A ⊂ B C – B ⊂ C – A

For any two sets, prove that:

A ∪ (A ∩ B) = A

Find sets A, B, and C such that A ∩ B, A ∩ C and B ∩ C are non–empty sets and A ∩ B ∩ C = ϕ.

For any two sets A and B, prove that: A ∩ B = ϕ A B’.

For any two sets, prove that:A ∩ (A ∪ B) = A