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.