Modus Ponens

The 'affirming mode': If P then Q, P is true, therefore Q is true.

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The 'affirming mode': If P then Q, P is true, therefore Q is true.

Modus Ponens (Latin for 'mode that affirms') is one of the most fundamental rules of inference in propositional logic. Given a conditional statement 'If P then Q' and the truth of the antecedent P, we can validly conclude Q. This rule is also called 'affirming the antecedent' and forms the basis of much deductive reasoning.

P → Q, P ⊢ Q

If it is raining, then the ground is wet. It is raining. Therefore, the ground is wet.
If you study hard, you will pass the exam. You study hard. Therefore, you will pass the exam.
If a number is divisible by 4, it is divisible by 2. 16 is divisible by 4. Therefore, 16 is divisible by 2.

How to recognize it

Look for an 'If...then...' statement (conditional)
Check if the 'if' part (antecedent) is affirmed as true
The conclusion will be the 'then' part (consequent)

Common mistakes

Affirming the consequent (invalid): 'If P then Q, Q is true, therefore P is true' - this does NOT follow
Example of the fallacy: 'If it rains, the ground is wet. The ground is wet. Therefore it rained.' (Wrong! Sprinklers could cause wet ground)

Step-by-step walkthrough

If it rains, the ground is wet. It is raining. What can we conclude?

Identify the conditional: 'If it rains, the ground is wet'
Check if the antecedent (if-part) is true: 'It is raining' = YES
Apply Modus Ponens: Since P is true, Q must be true
Conclude: The ground is wet

Answer: The ground is wet

Practice guidance

Logical Deduction