Some common rules of inference

3.1

p

Addition: -----

p?q

p?q p if n mod 6= 0, then n is even n mod 6 =0

Modus ponens: ----------- ----------------------------------------------------

q n is even

p?q ?q if you invite me, I’ll come I didn’t come

Modus tollens: ------------ -----------------------------------------------------

?p you didn’t invite me

p?q q?r

Hypothetical syllogism: --------------

p?r

p?q ?p

Disjunctive syllogism: -----------

q

p?q

Simplification: -----

p

p q

Conjunction: -----

p?q

Hypotheses

--------------

Conclusion

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