NIMCET 2015 Question Paper with solutions

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Question : 50 of 120

Marks: +1, -0

Let

P↖{-}

and

Q↖{-}

denote the complements of two sets Pand Q. Then the set (P - Q) ∪ (Q - P) ∪ (P ∩ Q) is :

P U Q
$P↖{-}$ ∪ $Q↖{-}$
P ∩ Q
$P↖{-}$ ∩ $Q↖{-}$

Solution:

We have,

(P-Q)∪(Q-P)∪(P∩Q)

⇒(P∩Q')∪(Q∩P')∪(P∩Q)

⇒(P∩Q')∪[(Q∩P')∪(Q∩P)]

⇒(P∩Q^{I})∪[Q∩(P∪P')]

⇒(P∩Q')∪(Q∩∪)

⇒(P∩Q')∪Q

⇒(P∪Q)∩(Q∪Q')

⇒(P∪Q)∩∪=(P∪Q)

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