LOGICAL EXPRESSIONS

In all the questions below, we consider generic propositions $P$ and $Q$ and $R.$

Is it true that not$(notP)$ is equivalent to $P?$ Explain your answer using a

truth$-$table with three columns $($one column for $P,$ one column for notP, and

one column for not$(notP)).$

Consider the following expression: $(P^{{?}^{?}}$notP$)=>Q.$ Does its truth$-$value

depend on the truth$-$value of $P?$ Why?

Write down truth$-$tables for the following expressions:

I. not$(P^{{?}^{?}}Q)$

II$.$ notPvvnotQ

III. not$(PvvQ)$

IV$.not{P}^{{?}^{?}}$notQ