Propositional Logic Terms

If p, then q
p
Therefore, q

If p, then q
p
Therefore, q

Valid, Modus Ponens

If p, then q
Not p
Therfore, Not q

Invalid, Denying the Antecedent

If p, then q
Not q
Therfore, Not p

Valid, Modus Tollens

If p, then q
q
Therfore, p

Invalid, Affirming the Consequent

p or q
Not q
Therefore, p

Valid, Disjunctive Syllogism

If p, then q
If q, then r
Therefore, if p, then r

Valid, Hypothetical Syllogism

p or q
p
Therfore, not q

Invalid, Affirming a Disjunct

If an argument is valid, then

if the premises are true, the conclusion must be true

Sound Argument

a valid argument with all true premises

unsound argument

either is invalid or has at least one false premise

The meaning of a statement is called

a proposition

Someone makes an argument when

they claim that the truth of their premises gives you logical reason to believe the conclusion.

An argument is invalid if

the conclusion could be false, even if the premises were true.

If X is a necessary condition for Y, then

Y cannot be true, unless X is true.

If X is a sufficient condition for Y, then

If X is true, Y must also be true.

Being a valid argument is a ______________________ condition for being a sound argument.

necessary

Having true premises is a ____________________________ condition for being a sound argument.

necessary

If a valid argument has a true conclusion, what do you know about the truth of the premises, if anything?

You cannot infer anything about the premises.

If a valid argument has true premises, what do you know about the conclusion?

The conclusion is true.

If a valid argument has a false conclusion, what do you know about the premises?

At least one of the premises must be false.

If a valid argument has false premises, what can you infer about the conclusion?

nothing

If an argument is invalid, does that mean it is unsound?

Yes, an invalid argument is an unsound argument.

If an argument has a false premise, does that mean it is unsound?

Yes, a sound argument must have all true premises.

Definition: a sound argument is _______________________

a valid argument with all true premises.

An argument's having a false premise is a sufficient/necessary/neither necessary nor sufficient condition for that argument's being unsound?

sufficient

An argument's being invalid is a _____________________ condition for it to be an unsound argument.

sufficient