Q2 of 162 Page 1

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

A ∩ (A ∪ B’) = ϕ

= A∩ (A ∪ B’)


= A∩( A’∩ B’) [By De–morgan’s law]


= (A ∩ A’) ∩ B’ [∴ A ∩ A’ = ϕ ]


= ϕ ∩ B’


= ϕ


=RHS


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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) = A ∩ B

 2

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

A – B = A Δ (A ∩ B)

 3

If A, B, C are three sets such that A ⊂ B, then prove that C – B ⊂ C – A.