Deductive Arguments

Modus Ponens:

1. If P then Q

2. P

Thus (3): Q

Modus Tollens:

3. If P then Q

4. ~Q (not Q)

Thus (3): Not P

Hypothetical Syllogism:

1. If P then Q

2. If Q then R

Thus (3): If P then R

Disjunctive Syllogism:

3. P or Q

4. ~P (not P)

Thus (3): Q

Dilemma:

1. P or Q

2. If P then R

3. If Q then S

Thus 4: R or S