Modus Tollens
A logical argument of the form:If P, then Q.
Latin:
removing by taking away.
Modus tollens Logic:
If P, then QNot P is true
Therefore Not Q is true
Using if A, then B, we have:
A = Not P and B = Not Q
P = antecedent and Q = consequent.
If antecedent = false, consequence = false.
Modus tollens Notation:
!P → !QTruth Table Modus tollens:
The fourth line of the table below shows Modus tollens| P | Q | P → Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
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What 7 concepts are covered in the Modus Tollens Calculator?
conjunctiona word used to connect clauses or sentences or to coordinate words in the same clausedisjunctiona 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 otherwiseequivalencethe state or property of being equivalent.modus tollensIf conditional statement if not p then not q!p --> !qnegationreverses the truth value of a given statement.
~propositiona declarative sentence that is either true or false (but not both)truth tablea 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.
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