 # Modus Ponens

## Modus Ponens

A logical argument of the form:
If P, then Q.
Latin:
a mode of affirming affirms.

## Modus Ponens Logic:

If P, then Q
P 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 Q
Not 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

P → Q

## Truth Table demonstrating Modus Ponens:

PQP → Q
TTT
TFF
FTT
FFT

### How does the Modus Ponens Calculator work?

Shows modus Ponens definition and examples

### What 1 formula is used for the Modus Ponens Calculator?

1. p --> q

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### 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.