[m4xr3sdEfault]*******,=,e \_ヾ(ᐖ◞ ) ID: 85a536 PROOF Q IS A LARP Nov. 19, 2018, 7:15 p.m. No.3967099   🗄️.is 🔗kun   >>7119 >>7420

In propositional logic, modus tollens (/ˈmoʊdəs ˈtɒlɛnz/; MT; also modus tollendo tollens (Latin for "mode that denies by denying")[1] or denying the consequent)[2] is a valid argument form and a rule of inference. It is an application of the general truth that if a statement is true, then so is its contra-positive.

 

The inference rule modus tollens validates the inference from

P

P implies

Q

Q and the contradictory of

Q

Q to the contradictory of

P

P.

 

The modus tollens rule can be stated formally as:

 

P

Q

,

¬

Q

¬

P

{\frac {P\to Q,\neg Q}{\therefore \neg P}}

where

P

Q

P\to Q stands for the statement "P implies Q".

¬

Q

\neg Q stands for "it is not the case that Q" (or in brief "not Q"). Then, whenever "

P

Q

P\to Q" and "

¬

Q

\neg Q" each appear by themselves as a line of a proof, then "

¬

P

\neg P" can validly be placed on a subsequent line. The history of the inference rule modus tollens goes back to antiquity.[3]

 

Modus tollens is closely related to modus ponens. There are two similar, but invalid, forms of argument: affirming the consequent and denying the antecedent. See also contraposition and proof by contrapositive.

 

The first to explicitly describe the argument form modus tollens was Theophrastus.[4]

[m4xr3sdEfault]*******,=,e \_ヾ(ᐖ◞ ) ID: 85a536 Nov. 19, 2018, 7:20 p.m. No.3967138   🗄️.is 🔗kun   >>7170

<<There are two similar, but invalid, forms of argument: affirming the consequent and denying the antecedent