This argument form is known as modus tollens and is logically valid because if the antecedent (P) is true and the consequent (Q) is false, then the negation of the antecedent (not P) must be true.

Using a truth table, we can determine that the proposition is false in all possible cases.

Logical connectives are words or symbols that connect propositions and determine the overall truth value of a compound proposition.

The converse of a proposition is formed by switching the antecedent and the consequent.

A syllogism is a logical argument that consists of two premises and a conclusion, where the conclusion is inferred from the premises.

Modus ponens is a rule of inference that allows us to infer the consequent (Q) from the antecedent (P) and the conditional statement (If P, then Q).

A tautology is a compound proposition that is true in all possible cases.

The negation of a proposition is a proposition that is true when the original proposition is false, and vice versa.

This argument form is known as disjunctive syllogism and is logically valid because if one of the disjuncts (P or Q) is true and the other (P) is false, then the remaining disjunct (Q) must be true.

Using a truth table, we can determine that the proposition is true in all possible cases.

Logical connectives are words or symbols that connect propositions and determine the overall truth value of a compound proposition.

The converse of a proposition is formed by switching the antecedent and the consequent.

A syllogism is a logical argument that consists of two premises and a conclusion, where the conclusion is inferred from the premises.

Modus tollens is a rule of inference that allows us to infer the negation of the antecedent (not P) from the conditional statement (If P, then Q) and the negation of the consequent (not Q).

A contradiction is a compound proposition that is false in all possible cases.