Modus Ponens
A logical argument of the form:
If P, then Q.
Latin:
a mode of affirming affirms.
Modus Ponens Logic:
If P, then QP is true
Therefore Q is true
P = antecedent and Q = consequent.
If antecedent = true, consequence = true.
Modus Ponens Example:
If it is Monday, John has to work.Today is Monday.
Therefore, John has to work
Modus Ponens Negation Logic:
If Not P, then Not QNot P is true
Therefore Not Q is true
Using if A, then B, we have:
A = Not P and B = Not Q
Modus Ponens Negation Example:
If it is not a weekend:John does not have to work.
Today is not a weekend.
Therefore, John does not have to work
Modus Ponens Notation:
P → QTruth Table demonstrating Modus Ponens:
| P | Q | P → Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
