Thread: Sets

Conclude that A=B if A,B, and C are sets such that?

(a) A U C= B U C

(b) A ∩ C = B ∩ C

a) No.

Becasue if A = {0}, B = {1} and C = {0,1}. Then A U C= B U C
but A <> B

(b) No.

Since A = {0}, B = {1} and C = {2}. Then A ∩ C = B ∩ C but A <> B

Would this be correct?

Yes.
Both are good counterexamples.