What's the difference between $\displaystyle \cap$ and $\displaystyle \wedge$, or $\displaystyle \cup$ and $\displaystyle \vee$?

So far I've interpreted $\displaystyle \wedge$ and $\displaystyle \vee$ as being used more in sentence structure, rather than for instance showing properties of sets. For instance would this be right?

$\displaystyle A=\lbrace 2,4,6 \rbrace \wedge B=\lbrace 4,5,6 \rbrace \implies A \cap B = \lbrace 4,6 \rbrace$