QuestionDetermine if the statement $$(p \wedge q) \wedge(\sim p \vee \sim q)$$ is a tautology, self-contradiction, or neither using a truth table.

Studdy Solution
Now, we can determine whether the statement is a tautology, a self-contradiction, or neither. A statement is a tautology if its truth value is true for all possible combinations of truth values of its propositional variables. A statement is a self-contradiction if its truth value is false for all possible combinations of truth values of its propositional variables. If a statement is neither a tautology nor a self-contradiction, its truth value is true for some combinations of truth values of its propositional variables and false for others.
Looking at the truth table, we can see that the truth value of the statement $(p \wedge q) \wedge(\sim p \vee \sim q)$ is false for all possible combinations of truth values of $p$ and $q$. Therefore, the statement is a self-contradiction.