Logic and Arguments Vocabulary

Vocabulary flashcards covering fundamental logical statements, argument structures, tautologies, contradictions, and validity definitions from the lecture notes.

Statement

Something that is either true or false

Biconditional statement

A conjunction of a conditional and its converse: If A, then B and if B, then A ($A \leftrightarrow B$)

Counterexample

One case that disproves a universal statement (all/every/always/etc.)

Logical equivalence (for statements)

2 statements are logically equivalent if and only if they have the same truth values

Tautology

A statement that's always true; the simplest example is $A \lor \sim A$

Contradiction

A statement that's always false; the simplest example is $A \cdot \sim A$

Premises (of an argument)

The assumptions/given statements. In everyday life, they are the basis, or starting points, for any argument; when you attack someone else's argument, you often attack the premises their argument is based on

Hypothesis and conclusion (of conditionals)

Hypothesis: the "if" part; Conclusion: the "then" part

Valid (for arguments)

An argument is valid if and only if the premises guarantee the conclusion. (If the premises are true, then the conclusion must be true.) Note: whether the premises are true or not in reality is irrelevant