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 |
How does the Modus Ponens Calculator work?
Free Modus Ponens Calculator - Shows modus Ponens definition and examples
What 1 formula is used for the Modus Ponens Calculator?
p --> q
What 7 concepts are covered in the Modus Ponens 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 ponens
- If conditional statement if p then 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.
