Modus Ponens - Justification Via Truth Table

Justification Via Truth Table

The validity of modus ponens in classical two-valued logic can be clearly demonstrated by use of a truth table.

p q p → q
T T T
T F F
F T T
F F T


In instances of modus ponens we assume as premises that p → q is true and p is true. Only one line of the truth table—the first—satisfies these two conditions (p and p → q). On this line, q is also true. Therefore, whenever p → q is true and p is true, q must also be true.

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