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Prove AnB subset A subset AUB?

In: Colleges and Universities, Proofs [Edit categories]

Answer:

I shall answer this under the assumption that 'n' means intersection.

Recall the definitions of intersection and union:

1) x is an element of AnB if and only if x is an element of A and x is an element of B
2) x is an element of AUB if and only if x is an element of A or x is an element of B

and recall that

3) X is an (improper) subset of Y if and only if every element of X is an element of Y

Thus, if x is an element of AnB, then x is an element of A and an element of B, so it clearly is an element A (law of simplification in logic). This implies AnB is a subset of A. Now if x is an element of A, it is certainly an element of A or an element of B (law of addition in logic), and therefore x is an element of AUB.

There are other ways of answering this based on axiomatic approaches.

First answer by Jrubin89. Last edit by Jrubin89. Contributor trust: 3 [recommend contributor ]. Question popularity: 3 [recommend question].

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