Modus ponens:
P > Q
P
------
Q
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Modus tolens:
P > Q
~Q
------
~P
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Hypothetical syllogism:
P > Q
Q > R
------
P > R
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Disjunctive syllogism:
P v Q
~P
------
Q
AND
P v Q
~Q
------
P
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MORE RULE OF INFERENCE TO COME