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I am struggling now for determining if the following statements are true or false. If the statement is true, then prove it. If not, make a counterexample.

Here are the statements:

- $A \subset B$ and $A \subset C$ if and only if $A \subset (B\cup C)$.
- $A \subset B$ or $A \subset C$ if and only if $A \subset (B\cap C)$.

My attemption:

Let A={1,2,3}, B={1,2,4}, and C={3}.

- I believe this is true. $A\subset B$ and $A\subset C$. Thus $A \subset (B\cup C)$ is true.
- I don't know how to begin.

Cbarker1