Prove that : A⊆B,B⊆C and C⊆ A⇒A=C.
We have A⊆B,B⊆C and C⊆ A, so A⊆B⊆C⊆A is a subset of B and B is a subset of C, so A is a subset of C, i.e., A⊆C
Also, C⊆A
Hence, A = C
If A, B and C be the sets such that A∪B=A∪C and A∩B=A∩C then prove that B= C
Prove that : (i) (A∪B)×C=(A×C)∪(B×C)
(ii) (A∩B)×C=(A×C)∩(B×C).