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Propositional Logic
Grinshpan
Modus ponens
Modus ponendo ponens (the way that affirms by affirming, mode that affirms, lat.)
or the law of detachment is a rule of inference, a method of proof.
From P and P → Q one concludes Q.
In words,
If P, then Q.
P is true.
Therefore Q is true.
In summertime fish are jumping and the cotton is high.
It0 s summertime.
So fish are jumping and the cotton is high.
In symbols,
P →Q
P
∴Q
or
((P → Q) ∧ P ) → Q
Note that the preceding compound proposition is a tautology.
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