# If P and Q are two sets such that P has 40 elements, P ∪ Q has 60 elements and P ∩ Q has 10 elements, how many elements does Q have?

Given:

n(P) = 40

n (P Q) = 60

n (P Q) =10

n(Q) = ?

We know,

n (P Q) = n(P) + n(Q) – n (P Q)

Substituting the values we get

60 = 40+n(Q)–10

60 = 30+ n(Q)

n(Q) =30

Q =has 30 elements.

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