# Operations/Proofs with Sets

Please show these proofs in great detail with all steps explained as they will serve as a template for future proofs.

1. Suppose A, B, and C are sets with A?B?C = 0. Prove or disprove: |AUBUC|= |A|+|B|+|C|.

2. Suppose A, B, and C are sets. Prove or disprove: AUB= A?B if and only if A=B.

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#### Solution Preview

1. Suppose A, B and C are sets with A?B?C=0 prove or disprove that |AUBUC|= |A|+|B|+|C|

The statement is false. Here I provide with you a counter example.

A={1, 2, 3, 4}, B={0, 1, 2}, C={0, 3, 4}

Clearly, there is no element in common for the three sets A, B and C. So, A?B?C=Ø.

Now we can find the union of three sets A, B and C, which contains the elements 0, 1, 2, 3, and 4. Namely, ...

#### Solution Summary

This solution helps with a problem regarding operations and proofs with sets.