Question

If p is any statement then (p $\lor$ -p) is a

• A. Contingency
• B. Contradiction
• C. Tautology
• D. None of these

Answer 1

Answer: (C)

Tautology

Answer 2

The given statement is $(p \lor \neg p)$. This statement is a logical disjunction (OR) between a proposition $p$ and its negation $\neg p$. According to the law of excluded middle, for any proposition $p$, either $p$ is true or its negation $\neg p$ is true. The logical OR operator ($\lor$) results in a true statement if at least one of its operands is true. Since either $p$ or $\neg p$ is always true, the statement $(p \lor \neg p)$ is always true, irrespective of the truth value of $p$. A statement that is always true for all possible truth values of its components is defined as a tautology.

The truth table for the statement $(p \lor \neg p)$ is as follows:

$p$	$\neg p$	$p \lor \neg p$
True	False	True
False	True	True

This table clearly shows that the statement $(p \lor \neg p)$ is true for all possible truth values of $p$, confirming it is a tautology.