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Luda [366]
3 years ago
6

Prove the following statements: S Subset S Union T T Subset S Union T S Intersection T Subset S S Intersection T Subset T.

Mathematics
1 answer:
muminat3 years ago
4 0

proofs:

<h2>S subset S Union T</h2>

We want to prove S \subset S \cup T

Let s\in S. By definition S\cup T is the set that contains the elements of T and the elements of S. Then s must be in  S\cup T. As s was arbitrary, we conclude that S \subset S \cup T.

<h2>T Subset S Union T</h2>

This proof is analogous to the previous one. In fact, this result is the same result as the previous one.

<h2>S Intersection T subset S </h2>

We want to prove S \cap T \subset S

Let y\in S\cap T. By definition of the intersection y should be in S and also in T. Then, we already saw that y\in S. As y was arbitrary we can conclude that S \cap T \subset S.

<h2>S Intersection T subset T</h2>

This is the same result as the previous one. There is no need to prove it anymore, but if you wish, you can reply the exact same proof.

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