Examine whether the following statement pattern is tautology, contradiction, or contingency: $p\vee \sim \left( p\wedge q \right)$

Hint: First, draw the truth table of the statement pattern given in the question. If for all the four cases the output is false, then its contradiction, if all outputs are true, then its tautology, else it is contingency.

Complete step-by-step answer:
Before moving to the options, let us discuss the meaning of different symbols used in the Boolean expression. See the symbols that we see in the Boolean expressions are called logic symbols, and this includes:
$\wedge $ - represents the AND logical operation.
$\vee $ - represents the OR logical operation.
$\sim $ - represents the NOT logical operator.
$\to $ - represents the if-then logical operator.
Now let us draw the truth-table of the above mentioned Boolean expression.
$p\vee \sim \left( p\wedge q \right)$

As it is clear from the truth-table that all the outputs are true, so we can say that the Boolean expression $p\vee \sim \left( p\wedge q \right)$ is a tautology.

Note: Be careful about the signs of AND operator and the OR operator, as students generally get confused among their symbols and make mistakes while solving. Also, be careful about the order of the If-then operator, as if-then operator is not commutative in nature. However, the order doesn’t matter in the case of the AND logical operator, and the OR logical operator as they are commutative in nature.