Modus Tollens - Justification Via Truth Table

Justification Via Truth Table

The validity of modus tollens can be clearly demonstrated through a truth table.

p q p → q
T T T
T F F
F T T
F F T

In instances of modus tollens we assume as premises that p → q is true and q is false. There is only one line of the truth table - the fourth line - which satisfies these two conditions. In this line, p is false. Therefore, in every instance in which p → q is true and q is false, p must also be false.

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