What does it mean for propositions to be in parenthesis without logical operators.

Question

i have stumbled upon this on one of my schools automatized tests.

In my universities discrete math 1 module: "Let P and Q be logic expressions, applying the laws of calculus prove the following:" (P v Q)(~P v Q)<=> Q

Do I multiply them? I can't find anything like this in any of my books.

here are some screenshots problem

supposed solution

Answer 1

I prefer $(P+Q)(\bar{P}+Q)$ rather than $(P \lor Q)\land(\lnot P \lor Q)$. Hence, the logical steps follow:

\begin{equation} \begin{aligned} (P+Q)(\bar{P}+Q) \, = & \, \overbrace{P\bar{P}}^{0}+PQ+\bar{P}Q+QQ &\\ =& \, \underbrace{(P + \bar{P} + Q)}_1 \, Q &\\ = & \, Q & \blacksquare \end{aligned} \end{equation}