Q2 of 162 Page 1

For any two sets A and B, prove the following:

A – (A – B) = A ∩ B

For any sets A and B we have De morgans law


(A ∪B)’ =A’ ∩B’ , (A ∩ B)’ = A’ ∪ B’


=A – (A–B)


= A ∩ (A–B)’


= A∩(A∩B’)’


= A∩(A’∪ B’)’)


= A ∩ (A’∪B)


= (A ∩ A’) ∪ (A ∩ B)


= ϕ ∪ (A ∩ B)


= (A ∩ B)


More from this chapter

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1

For any two sets A and B, prove that: A’ – B’ = B – A

 2

For any two sets A and B, prove the following:

A ∩ (A’ ∪ B) = A ∩ B

 2

For any two sets A and B, prove the following:

A ∩ (A ∪ B’) = ϕ

 2

For any two sets A and B, prove the following:

A – B = A Δ (A ∩ B)