If A, B, C are three sets such that A⊂B, then prove that C−B⊂C−A
We have , ACB
To show : C−B⊂C−A
Let, x ϵ C−B
⇒x ϵ C and x/ϵA [∵A⊂B]
⇒x ϵ C−A
Thus, x ϵ C−B⇒x ϵC−A
This is true for all x ϵC−B
∴C−B⊂C−A
If A, B and C be the sets such that A∪B=A∪C and A∩B=A∩C then prove that B= C
If A, B and C be three non empty sets given in such a way that A×B=A×C, then prove that B = C.