# Prove that $P \cup Q = Q$ and $P \cap Q = P$ if $P$ is a subset of $Q$

When $P$ is a subset of $Q$, use logical connectives to

1. Prove $P \cup Q = Q$.

2. Prove $P \cap Q = P$.

I know that they are true, but I don't know how to use the definitions of union and intersection in terms of logical connectives to prove them.

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One half of your question was asked here: Prove that $A \subset B$ if and only if $A \cap B = A$. Several other equivalent conditions were given here: Statements equivalent to $A\subset B$ –  Martin Sleziak Sep 30 '13 at 15:42