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Question

If set C is the super set of sets A and B and A B then prove that (C - B) (C-A).

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Solution

It is given that set C is the superset of sets A and B.
These means that A and B are subsets of C, i.e., AC and BC.
Also, it is given that A B.
i.e., A BC
This can be shown in the following Venn diagram:




(C−B) indicates those elements of C that do not belong to B.



(C−A) indicates those elements of C that do not belong to A.



Hence, we can see from that (C-A) consists of (C-B).
∴ (C-B)(C-A)

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