Q2 of 162 Page 1

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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