Modus Tollens

A logical argument of the form: If P, then Q. The Latin translation is roughly, removing by taking away.

Modus tollens Logic:

If P, then Q
Not P is true
Therefore Not Q is true
Using if A, then B, we have A = Not P and B = Not Q

P is the antecedent and Q is the consequent. If the antecedent is not true, the consequence is not true.

Modus tollens Notation:

!P → !Q

Truth Table demonstrating Modus tollens:

The fourth line of the table below shows Modus tollens
PQP → Q
TTT
TFF
FTT
FFT

How does the Modus Tollens Calculator work?

Shows Modus Tollens definition and examples

What 1 formula is used for the Modus Tollens Calculator?

  1. !p --> !q

For more math formulas, check out our Formula Dossier

What 7 concepts are covered in the Modus Tollens Calculator?

conjunction
a word used to connect clauses or sentences or to coordinate words in the same clause
disjunction
a binary connective classically interpreted as a truth function the output of which is true if at least one of the input sentences (disjuncts) is true, and false otherwise
equivalence
the state or property of being equivalent.
modus tollens
If conditional statement if not p then not q
!p --> !q
negation
reverses the truth value of a given statement.
~
proposition
a declarative sentence that is either true or false (but not both)
truth table
a table that shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it is constructed.

Modus Tollens Calculator Video


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