Given that n(p) = 19, m(P $\cup$ Q) = 38 and n(P $\cap$ Q) = 7, Find n(C)

The question has a typo: "n(C)" should almost certainly be n(Q), and "m(P ∪ Q)" should be n(P ∪ Q). I'll work with that reading.

Concept

For two sets, the union formula is:

n(P ∪ Q) = n(P) + n(Q) − n(P ∩ Q)

Solution

Given:

• n(P) = 19
• n(P ∪ Q) = 38
• n(P ∩ Q) = 7

Substitute into the formula:

38 = 19 + n(Q) − 7

38 = 12 + n(Q)

n(Q) = 38 − 12 = 26

Answer

n(Q) = 26, which is option A.

Tip: Always write out the formula n(P ∪ Q) = n(P) + n(Q) − n(P ∩ Q) first, then rearrange it to find the missing value. Subtracting the intersection avoids counting the overlap twice. Also, if a question has a typo like this one, check which option fits the most sensible reading, here n(Q).