RULE OF INFERENCE: IMPLICATION
RULE OF INFERENCE AND REPLACEMENT: ( and ≡
A conditional asserts that the truth of one claim (the antecedent) forces the truth of the other (the consequent). As a result, if we know that the antecedent is true, then we also know that the consequent is true (Modus Ponens). In addition, since the truth of the antecedent forces the truth of the consequent, if we know that the consequent is false, we know that the antecedent must also be false (Modus Tollens).
MODUS PONENS MODUS TOLLENS
Given p כ q and p Given p כ q and ~q
we can deduce q we can deduce ~p
HYPOTHETICAL SYLLOGISM CONSTRUCTIVE DILEMMA
Given p כ q and q כ r Given p V q and p כ r and
q כ s
we can deduce p כ r
we can deduce r V s
RULES OF REPLACEMENT: ( and ≡
TRANSPOSITION EXPORTATION
The formula p כ q The formula (p & q) כ r
can (1) replace or can (2) can (1) replace or can (2)
be replaced at any time be replaced at any time
during a deduction by during a deduction by
~q כ ~p. p כ (q. כ r)
(modus tollens)
IMPLICATION EQUIVALENCE
The formula p כ q The formula p ≡ q
can (1) replace or can (2) can (1) replace or can (2)
be replaced at any time be replaced at any time
during a deduction by during a deduction by
~p V q (p כ q) & (q כ p)
and (p &q) V (~p & ~q)
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