Q9 of 162 Page 1

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

Let x be any element of Set A

And y be any element of Set B

Now x≠y A ∩ B = ϕ

This means no element of B should be in A.

Thus, x is an element of A and an element of B’

As x ϵ B’

A B’

Hence, Proved.

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.

If A and B are sets, then prove that A – B, A ∩ B and B – A are pair wise disjoint.

Using properties of sets, show that for any two sets A and B, (A ∪ B) ∩ (A ∪ B’) = A.