Final answer:
To find n(U), the number of elements in the universal set U, sum the number of elements in the union of sets P and Q (n(PUQ)) and the number of elements not in that union (n(PUQ)'). Using the given values, we find that n(U) equals 105.
Step-by-step explanation:
The student's question asks to find the value of n(U), which stands for the number of elements in the universal set U, given certain information about sets P and Q and their union. We are given n(P)=45, n(Q)=55, and the number of elements in the union of P and Q, which is n(PUQ)=90. We are also given the number of elements that are not in P U Q, which is n(PUQ)'=15.
To find n(U), we need to recognize that the universal set includes all elements in both P, Q, and any elements not in their union. Thus, n(U) is the sum of n(PUQ) and n(PUQ)'.
Using the information provided, we calculate n(U) as follows:
n(U) = n(PUQ) + n(PUQ)'
= 90 + 15
= 105
So, the number of elements in the universal set U is 105.