For all sets A and B, A – (A ∩ B) is equal to ______________.

Question

Fill in the blanks:

For all sets A and B, A – (A ∩ B) is equal to ______________.

Answer 1

A ∩ B’

Given: A and B are two given sets

To find: A – (A ∩ B)

A – (A ∩ B)

= A ∩ (A ∩ B)’

{∵ A – B = A ∩ B’}

= A ∩ (A’ ∪ B’)

{∵ (A ∩ B)’ = A’ ∪ B’}

= (A ∩ A’) ∪ (A ∩ B’)

{∵ Distributive property of set: (A ∩ B) ∪ (A ∩ C) = A ∩ (B ∪ C)}

= Φ ∪ (A ∩ B’)

{∵ A ∩ A’ = Φ}

= A ∩ B’

A – (A ∩ B) = A ∩ B’