Construct the truth table for each of the following statement patterns.

$\left(q\to p\right)\vee \left(~p\leftrightarrow q\right)$

Construct the truth table for each of the following statement patterns.

$\left[p\to \left(q\to r\right)\right]\leftrightarrow \left[\left(p\wedge q\right)\to r\right]$

Construct the truth table for each of the following statement patterns.

$p\to \left[~\left(q\wedge r\right)\right]$

Construct the truth table for each of the following statement patterns.

$\left(p\vee ~q\right)\to \left(r\wedge p\right)$

Using truth tables prove the following logical equivalences.

$~p\wedge q\equiv \left(p\vee q\right)\wedge ~p$

Using truth tables prove the following logical equivalences.

$~\left(p\vee q\right)\vee \left(~p\wedge q\right)\equiv ~p$

Using truth tables prove the following logical equivalences.

$p\leftrightarrow q\equiv ~\left[\left(p\vee q\right)\wedge ~\left(p\wedge q\right)\right]$

Using truth tables prove the following logical equivalences.

$p\to \left(q\to p\right)\equiv ~p\to \left(p\to q\right)$

Using truth tables prove the following logical equivalences.

$\left(p\vee q\right)\to \mathrm{r}\equiv \left(p\to r\right)\wedge \left(q\to r\right)$