If P and Q are two sets such that n(P ∪ Q) = 75, n (P ∩ Q) = 17 and n(P) = 49, find n (Q).

Question

Philoid · Accepted Answer

Given:

n(P) = 49

n(P ∪ Q) = 75

n(P ∩ Q) = 17

To Find: n(Q)

We know that,

|A ∪ B| = |A| + |B| - |A ∩ B| (where A and B are two finite sets)

Therefore,

n(P ∪ Q) = n(P) + n(Q) – n(P ∩ Q)

75 = 49 + n(Q) - 17

n(Q) = 75 – 49 + 17 = 43

Therefore,

n(Q) = 43