1) We have to find the complement of B, within U.
We have B = {a, b, c, d}
So the elements of the universe U that do not belong to B (therefore belong to the complement of B) are:
B' = {e, f, g}
2) We have
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4, 5}
B = {1, 3, 5, 7}
We have to find the number of elements in (Ac intersects Bc).
We start by looking at the complements of A and B:
A' = {3, 6, 7}
B' = {2, 4, 6}
If we intersect this two groups, only the element "6" stays, so the number of elements we are looking for is 1.
4) We have to find the intersect between A and B
A = {a, c, e, g}
B = {a, b, c, d}
There the intersection group will have only the elements that are in both groups.
In this case we have:
A intersects B = {a, c}
5) the universe is the integers from 1 to 7 included.
B = {1, 3, 5, 7} ... the odd numbers within the universe U.
We have to calculate the complement of B (B'), so we have to look at the elements that are in the universe U and not in the group B:
B' = {2, 4, 6}
There are 3 elements in the complement of B.