What is the meaning of  $\bigvee$ (bigvee) operator What do mean $\bigvee$  operator in page 6 of this document.
It is a Variable-sized Math Operator.
What about $\bigwedge$?
 A: If you have an indexed family of propositions, say $\{P_\alpha\}_{\alpha \in I}$, then 
$$\bigvee_{\alpha\in I} P_{\alpha}$$ is the proposition that at least one $P_{\alpha}$ is true.  This could also be used for maxima or minima.  Another guise might be
$$\bigvee_{k=1}^n f_k$$
to express the maximum of $f_1, f_2, \cdots , f_n$.
A: "Wedges and vees" ($\wedge,\vee$) are usually used to denote "meets and joins" (respectively) in lattice theory. Roughly speaking "meet" means "greatest lower bound" and "join" means "least upper bound".
This will come up in logic too because logical conditionals have interpretations as"meets and joins".
As you can see in the document page 6, it looks like they are translating 1.2/1.3/1.4  to 1.5/1.6/1.7. I am very suspicious that there is a typo, because in one spot they have replaced $\cup$ with $\vee$ (and that makes sense, since $\cup$ is a join operator for the lattice of subsets of a set), but they also did the same for $\cap$. 
I think possibly they should have replaced $\cap$ with $\wedge$. ($\cap$ is of course, the meet operator in the lattice of subsets of a set.)
