Question

Prove : A ∩ (A ∪ B)’ = Ф

Answer 1

According to De Morgan's Laws,

• (A ∪ B)' = A' ∩ B'
• (A ∩ B)' = A' ∪ B'

Now, according to the above,

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

[Associative Law]

Then we have

∅ ∩ B' = ∅

[Identity of Sets]

For your information,

we can show De Morgan's Laws with the Benn Diagram.

The laws of set theory:

• Communicative

• Associative

• Distributive

• Double Complement

• De Morgan's Laws

• Domination

• Idempotent