Let P and Q be two sets then what is (P∩Q′)∪(P∪Q)′ equal to ?
A
(P∩Q′)∪(P∪Q)′=ξ∩Q′=ξ∩Q′=ξ
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B
(P∪Q′)∪(P∪Q)′=ξ∩Q′=ξ∩Q′=ξ
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C
(P∩Q′)∪(P∩Q)′=ξ∩Q′=ξ∩Q′=ξ
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D
none of the above
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Solution
The correct option is B(P∩Q′)∪(P∪Q)′=ξ∩Q′=ξ∩Q′=ξ (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