SOLUTION
U is the universal set given as
U = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
and set A = [1, 3, 5, 7, 9] and B = [4, 5, 6, 7]
(a) A' means A prime or A compliment. That means the element in the universal set U, that is not in set A. And this becomes
A' = [2, 4, 6, 8, 10] that is all even numbers
(b) A n B means A intersection B, that is the elements that is "common" to both A and B
A n B = [5, 7]. Only 5 and 7 is common to both A and B
(c) A n B'. We have to find B' first
B' = [1, 2, 3, 8, 9, 10]. That is elements in set U that are not in set B
So, A = [1, 3, 5, 7, 9] and B' = [1, 2, 3, 8, 9, 10]
A n B' = [1, 3, 9]
(d) A' u (A n B) means A' union (A n B). It indicates elements you can see in both A' and (A n B) together. But the elements should not be repeated.
A' = [2, 4, 6, 8, 10] and A n B = [5, 7]
A' u (A n B) = [2, 4, 5, 6, 7, 8, 10]