Are the following conditional statements tautologies? 

Truth table for the conditional statement $p\wedge q\Rightarrow p\vee q$

Since all the truth values of the conditional 

$p\wedge q\Rightarrow p\vee q$ are T, it is a tautology

(b) Truth table for the conditional statement

$p\wedge q\Rightarrow \sim p$ is as follows :

Since all truth values of the conditional $p\wedge q\Rightarrow \sim p$ are neither T nor F so it is neither a tautology nor a contradiction. 

(c) Let us prepare the truth table for the conditional $\left\{\right(p\Rightarrow q)\vee p\}\wedge q\Rightarrow q$

Let $l=\left\{\right(p\Rightarrow q)\vee p\}\wedge q$ Then we have

Thus the statement $l=q\text{ i.e., }\left\{\right(p\Rightarrow q)\vee p\}\wedge q\Rightarrow q$  has its truth value T for all its entries in the truth table. Hence, it is a tautology.

(d) We have to examine the statement

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

Let $l=(p\wedge q)\Rightarrow p\text{ and }m=q\wedge ~q$

Then we have to examine the statement $l\Rightarrow m$ We now prepare the truth table for the conditional $l\Rightarrow m$

Since all the truth values of the statement $I\Rightarrow m$are not T, it is not a tautology. In fact, the statement

has its truth value F for all its entries in the truth table, it is a contradiction.$I\Rightarrow m$