Step 1 :Define the sets A, B, and C as A = {'u', 'w', 'y', 's', 'q'}, B = {'y', 's', 'q', 'z'}, and C = {'w', 'y', 'v', 'z', 'x'} respectively.
Step 2 :Find the complement of set B, which includes all elements not in set B. The complement of B is {'u', 'x', 'v', 'w'}.
Step 3 :Find the intersection of set A and the complement of set B. The intersection includes all elements that are in set A and not in set B. The intersection of A and B' is {'u', 'w'}.
Step 4 :Find the intersection of set A and set C. The intersection includes all elements that are common to both sets. The intersection of A and C is {'w', 'y'}.
Step 5 :Find the complement of the intersection of set A and set C. The complement includes all elements not in the intersection. The complement of the intersection of A and C is {'u', 'v', 's', 'z', 'x', 'q'}.
Step 6 :The elements in the set \(A \cap B'\) are \(\boxed{\{u, w\}}\) and the elements in the set \((A \cap C)'\) are \(\boxed{\{u, v, s, z, x, q\}}\).