Welcome to Math Help Forum!This statement gives us the 22 outside the three set loops.There are altogether 22 elements in the intersection of the complements of these three sets.Initially I wrote in the intersection of B and C (where the 16 is now), and therefore in the area representing (where the 15 is) and in (where the 18 is).Set B contains 31 elements whereas the intersection of A and C has 34 elements.This is potentially ambiguous. What does "The number of elements in A and C but not in B" mean? I am assuming it means "The number of elements that are in A and in C but not in B"; in other words the number of elements in . And I'm also assuming that "the number in A and C" means the number that are in A and in C; in other words the number in , which (we've been told) is 34. So:The number of elements in A and C but not in B is one more than half the number in A and C.
So this gives us , and the 15 in .Initially I wrote in (where the 10 is now); and therefore I wrote in (where the 14 is). So I was then able to total up the numbers, and put the result equal to 95. This gave:The number of elements in C, not in A and not in B is 4 more than the number of elements in A, not in C and not in B.
So those are my answers, which I believe to be correct based on the assumption that I have interpreted the phrase "the number in A and C but not in B" correctly.