Question

Let A and B be two finite sets such that n(P and Q) = 20, n(P –Q) = 14, n(Q –P) = 26.Then find n(P) + n(Q)

Answer 1

SOLUTION

GIVEN

P and Q be two finite sets such that

n(P and Q) = 20, n(P - Q) = 14, n(Q - P) = 26

TO DETERMINE

The value of n(P) + n(Q)

EVALUATION

Here it is given that P and Q be two finite sets such that n(P and Q) = 20 , n(P - Q) = 14 , n(Q - P) = 26

n(P and Q) = 20

⇒ n(P ∩ Q) = 20

Now

n(P - Q) = 14

⇒ n(P) - n(P ∩ Q) = 14

⇒ n(P) - 20 = 14

⇒ n(P) = 34

Again

n(Q - P) = 26

⇒ n(Q) - n(P ∩ Q) = 26

⇒ n(Q) - 20 = 26

⇒ n(Q) = 46

∴ n(P) + n(Q) = 34 + 46 = 80

FINAL ANSWER

n(P) + n(Q) = 80

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