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