Question

Suppose A, B, and C are sets. In at least one of the following situations, one can conclude that A = B.
Identify those cases where this conclusion does apply.

(i) A ∪ C = B ∪ C
A={1,2},A={1,2}, B={2,3}B={2,3} and C={1,2,3}.C={1,2,3}. It is A∪B=A∪C=C={1,2,3}.A∪B=A∪C=C={1,2,3}. However, A≠B.

(ii) A ∩ C = B ∩ C
={1,2},A={1,2}, B={2,3}B={2,3} and C={2}.C={2}. It is A∩B=A∩C=C={2}.A∩B=A∩C=C={2}. But, A≠B.

(iii) A ∪ C = B ∪ C and A ∩ C = B ∩ C

Need help with (iii)
Thanks

Answer 1

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