Logic Final- Compound Syllogisms

> stands for the hypothetical symbol; v stands for the disjunctive symbol; :. stands for therefore

Pure hypothetical format

A —> B

B —> C

A —>C

mixed hypothetical format

if A then B

affirm/deny syllogism

conclusion

modus tollens

p > q

~q

:. ~p

modus ponens

p > q

p

:. q

affirming the consequent (invalid hypothetical)

p > q

q

:. p

denying the antecedent (invalid hypothetical)

p > q

~p

:. ~ q

valid disjunctive case

p v q

~ p

:. q

p v q

~q

:. p

disjunctive exception case (exclusive domain)

p v q

p

:. ~q

invalid disjunctive case

p v q

p

:. ~q

p v q

~p

:. ~q

conjunctive form (1 of 2)

(p & q)

~(p & q)

valid conjunctive case

~(p & q)

p

:. ~q

~(p & q)

q

:. ~p

invalid conjunctive case

~ (p & q)

~p

:. q

~(p & q)

~q

:. p

What does “P” represent in a hypothetical syllogism?

antecedent

what does “Q” represent in a hypothetical syllogism?

consequent

What phrase describes a disjunctive syllogism best?

Either or

what phrase describes a conjunctive syllogism best?

Both and

disjunctive syllogisms must have 1 ___ premise and a _____ conclusion

negative (denied); positive

Stong disjunctive

only P or Q can be true/false at one time (exclusive)

Weak disjunctive

both P and Q could be true/false at the same time