Question

Use the properties of sets to prove that for all the sets A and B, A – (A ∩ B) = A – B​

Answer 1

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A – (A ∩ B) = A ∩ (A ∩ B)′ (since A – B = A ∩ B′)

= A ∩ (A′ ∪ B′) [by De Morgan’s law)

= (A∩A′) ∪ (A∩ B′) [by distributive law]

= φ ∪ (A ∩ B′)

= A ∩ B′ = A – B

Hence proved that A – (A ∩ B) = A – B.

Answer 2

Answer:

Step-by-step explanation:

A – (A ∩ B) = A ∩ (A ∩ B)′ (since A – B = A ∩ B′)

= A ∩ (A′ ∪ B′) [by De Morgan’s law)

= (A∩A′) ∪ (A∩ B′) [by distributive law]

= φ ∪ (A ∩ B′)

= A ∩ B′ = A – B

Hence proved