Logic Exam 1

Soundness

An argument is sound if and only if it’s valid, and its premises are all true.

Validity

An argument is valid if and only if there’s no possible world where the premises are all true and the conclusion false.

~ (tilde)

Negation/Not

. (dot)

Conjunction/And

v (wedge)

Or

Horseshoe

if/then and only if

Tribar

If and only if/just in case

Dot truth table

T, F, F, F

Wedge truth table

T, T, T, F

Horseshoe truth table

T, F, T, T

Tribar truth table

T, F, F, T

Tautologies

A sentence is a ____ if and only if it is true in all possible worlds

Contradictions

A sentence is a ____ if and only if it is false in all possible worlds

Contingencies

A sentence is a ____ if and only if it is true in some possible worlds and false in others.

Logical Equivalence

Two sentences are ____ if and only if there is no possible world where they differ in truth-value.

Logical Implication

There is no possible world where p is true and q false.

Consistency

A set of formulae is ____ if and only if there is at least one possible world where they are all true.

Invalidity

An argument is ____ if and only if there is at least one possible world where the premises are true and the conclusion false.