Definition: A formula is said to be a Tautology if every truth assignment to its component statements results in the formula being true. A formula is said to be a Contradiction if every truth assignment to its component statements results in the formula being false.

It is easy to tell whether a formula is a tautology, contradiction, or neither by first constructing the truth table for the formula and examining the far right column. If the far right column contains only true then the formula is a tautology. If the far right column contains only false then the formula is a contradiction. Otherwise, the formula is neither a tautology or a contradiction. Let's look at a few examples

Let $P$ and $Q$ be statements and consider the formula:

(1)
\begin{align} \quad (P \wedge \neg P) \rightarrow Q \end{align}

We construct the truth table for this formula:

$P$ $Q$ $\neg P$ $(P \wedge \neg P)$ $(P \wedge \neg P) \rightarrow Q$
T T F F T
T F F F T
F T T F T
F F T F T

We look at the far right column of the truth table and see all trues. Therefore $(P \wedge \neg P) \rightarrow Q$ is a tautology.

For an example of a contradiction, consider the formula $(P \vee \neg P) \rightarrow (Q \wedge \neg Q)$. It is easy to see that $P \vee \neg P$ is true for all truth assignments to $P$. Furthermore, it is easy to see that $Q \wedge \neg Q$ is false for all truth assignments to $Q$. Therefore it must be that this formula results in falsehood for all truth assignments to $P$ and $Q$. So $(P \vee \neg P )\rightarrow (Q \wedge \neg Q)$ is a contradiction.