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?
We have,
n (P) = 40
n (P ∪ Q) = 60
n (P ∩ Q) =10
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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