2
Question
For all sets A and B, B – (A ∩ B) is equal to ____________.
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Solution
For set A and B
B – (A ∩ B) = B ∩ (A ∩ B)' (By defination of negation)
= B ∩ (A' ⋃ B')
= (B ∩ A') ⋃ (B ∩ B')
= (B ∩ A') ⋃ ϕ
= B ∩ A'
= B ∩ A'
= B – A
Hence, B – (A ∩ B) = B – A
B – (A ∩ B) = B ∩ (A ∩ B)' (By defination of negation)
= B ∩ (A' ⋃ B')
= (B ∩ A') ⋃ (B ∩ B')
= (B ∩ A') ⋃ ϕ
= B ∩ A'
= B ∩ A'
= B – A
Hence, B – (A ∩ B) = B – A= (B ∩ A') ⋃ (B ∩ B')
= (B ∩ A') ⋃ ϕ
= B ∩ A'
= B ∩ A'
= B – A
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