If A and B are sets such that A C B C then can you conclude

If A and B are sets such that A C = B C then can you conclude that A = B. Justify your answer.

Solution

No, Its false A is Not equal to B

A = {1} , B = {0} . and C = {0,1}

Then AUC = {0,1} AND Then AUB = {0,1} but A is not equal to B

Consider the case when A and B are both subsets of A but are not equal.
Answer: False