Answer:
draw 2 intersecting circles inside a rectangle
the circle on the left is A
the circle on the right is B
the rectangle is the universe U
U contains 32 elements
A contains 11 elements
B contains 17 elements
AUB contains 25 elements
this means there are 7 elements (32-25) not in A or B (32 elements in the universe)
the number of elements in A is 11 and the number of elements in B is 17
if A and B were disjoint, not intersecting, then AUB would contain 28 elements
but because AUB contains 25 elements, that means A and B intersect and there are 28-25=3 elements in A∩B
there are 8 elements in A only, 3 elements in A and B (their intersection), and 14 elements in B only
(8+3+14=25 which is how many elements in AUB)
n(AUB') means all the elements in the universe that are not in B
there are 8 in A only and 7 in the universe that are not in A or B for a total of 15 elements in AUB'
(you can't use the 3 in the intersection because they are in B as well as A and you can't use the 14 that are in B)
n(A'∩B')=n(AUB)' which is one of DeMorgan's Laws
n(AUB)=25 so n(AUB)'=everything in the universe not in A or B which is 7 elements (remember that n(U)=32 and AUB=25 so 32-25=7
n(A∩B)=3 which we already determined from above
Explanation: