Q. 24.2( 5 Votes )

# If P and Q are two sets such that n(P ∪ Q) = 75, n (P ∩ Q) = 17 and n(P) = 49, find n (Q).

Answer :

Given:

n(P) = 49

n(P Q) = 75

n(P Q) = 17

To Find: n(Q)

We know that,

|A B| = |A| + |B| - |A B| (where A and B are two finite sets)

Therefore,

n(P Q) = n(P) + n(Q) – n(P Q)

75 = 49 + n(Q) - 17

n(Q) = 75 – 49 + 17 = 43

Therefore,

n(Q) = 43

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RS Aggarwal - Mathematics