If n(P) = 20 and n(Q) = 30 and n(PuQ) = 40, find the value n(PnQ)

The values n(P), n(Q), n(PuQ), and n(PnQ) represent the number of elements in the sets P, Q, the union of sets P and Q, and the intersection of sets P and Q, respectively. To find n(PnQ), we need to figure out how many elements are in both sets P and Q. This is because the intersection of two sets only includes the elements that are present in both sets. We can use the formula n(PuQ) = n(P) + n(Q) - n(PnQ) to find n(PnQ). Plugging in the given values, we get: 40 = 20 + 30 - n(PnQ) Solving for n(PnQ), we get: n(PnQ) = 20 + 30 - 40 = 10 So the answer is 10.