CH02_3_CompoundStatement

Argument

A sequence of statements, where the final statement is the conclusion.

Premise

A statement or assumption that forms the basis for an argument, except for the final one.

Conclusion

The final statement in an argument, which follows from the premises.

Valid Argument Form

An argument form where if the premises are true, the conclusion must also be true.

Truth Table

A table used to determine the truth values of premises and conclusions in logical arguments.

Critical Row

A row in a truth table where all premises are true.

Modus Ponens

An argument form: If p then q, p, therefore q.

Modus Tollens

An argument form: If p then q, not q, therefore not p.

Rule of Inference

A valid form of argument used in logical reasoning.

Fallacy

An error in reasoning that results in an invalid argument.

Converse Error

An invalid argument form that occurs when "If p, then q" is mistakenly reversed to "If q, then p." For example, "If it's raining, the ground is wet. The ground is wet. Therefore, it's raining" is a converse error because the ground could be wet for other reasons.

Inverse Error

Inverse error occurs when "If p, then q" is incorrectly negated to "If not p, then not q."

Contradiction Rule

If the assumption that a statement is false leads to a contradiction, the statement is true.

Knight

A person who always tells the truth in logical puzzles.

Knave

A person who always lies in logical puzzles.

Syllogism

An argument form consisting of two premises and a conclusion.

Generalization

An inference that extends a conclusion from a specific case to a more general one.

Specialization

An argument that focuses on a specific instance from a general case.

Elimination

A form of reasoning that concludes a result based on ruling out other possibilities.

Transitivity

The logical principle that if p implies q and q implies r, then p implies r.

Argument Form

A sequence of statement forms with symbols representing statements.

Invalid Argument Form

An argument form where the conclusion may be false even if premises are true.

Disjunctive Syllogism

Another valid argument form: "p or q. Not p. Therefore, q."