Let AB and C be nonempty subsets of a universal set U Dispro

Let A,B, and C be nonempty subsets of a universal set U. Disprove the following statements:

(a) If AB=AC ,then B=C.
(b) If AB=CB,then implies A=C.

(c) If A is not a subset of B and B is not a subset of A,then AB=.

Solution

a. A={1,2,3} B={3,5}, C={3,8} AB=AC but B is not equal to C

b. A={1,2,3} B={3,5}, C={1,2,5} AB=CB={1,2} but A is not equal to C

c. A={1,2,3} B={3,5} A is not a subset of B and B is not a subset of A.

AB=3 not null.