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Let P and Q be two sets, then what is ( P ∩ Q′) ∪ (P∪ Q)′ equal to ?

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Let P and Q be two sets, then what is ( P ∩ Q′) ∪ (P ∪ Q)′ equal to ?

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( P ∩ Q′) ∪ (P ∪ Q)′ = ( P ∩ Q′) ∩ (P′ ∩ Q′) 

= ( P ∪ P′) ∩ (P ∪ Q′) ∩ (Q′ ∪ P′) ∩ (Q′ ∪ Q′) 

= ξ ∩ { Q′ ∪ (P ∩ P′)} ∩ Q′ 

= ξ ∩ { Q′ ∪ ξ) ∩ Q′ 

= ξ ∩ Q′ ∩ Q′ = ξ ∩ Q′= ξ

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