The symbol $\vee$ usually denotes the logical disjunction (the OR truth-functional operator), just as $\wedge$ usually denotes logical conjunction (the AND truth-functional operator).
The empty operator probably refers to logical conjunctions as well, and the upper bar should refer to logical negation.
As suggested by @Joffysloffy, you can map these to operators on variables with values in $\\{ 0, 1 \\}$, $F$ mapping to $0$ and $T$ mapping to $1$, with (lacking notation rigor) :
$$ x \wedge y = xy $$ $$ x \vee y = x + y - xy $$
(The latter is to be compared with $\left\vert{A \cup B}\right\vert = \left\vert{A}\right\vert + \left\vert{B}\right\vert - \left\vert{A \cap B}\right\vert$)