Argument Validity Checker
A valid argument is one where the conclusion must be true if the premises are true. Enter P1, P2, and conclusion — this tool identifies the argument form and checks structural validity.
Common Valid Argument Forms
Modus Ponens
Affirming the antecedent
P1: If P, then Q
P2: P is true
∴ Q is true
P2: P is true
∴ Q is true
If it rains, the ground is wet. It is raining. ∴ The ground is wet.
Modus Tollens
Denying the consequent
P1: If P, then Q
P2: Q is false
∴ P is false
P2: Q is false
∴ P is false
If he studied, he'd pass. He didn't pass. ∴ He didn't study.
Hypothetical Syllogism
Chain of conditionals
P1: If P, then Q
P2: If Q, then R
∴ If P, then R
P2: If Q, then R
∴ If P, then R
If X, then Y. If Y, then Z. ∴ If X, then Z.
Categorical Syllogism
Barbara (All A, All B)
P1: All A are B
P2: All B are C
∴ All A are C
P2: All B are C
∴ All A are C
All humans are mortal. All Greeks are human. ∴ All Greeks are mortal.
Disjunctive Syllogism
Denying the disjunct
P1: P or Q
P2: Not P
∴ Q
P2: Not P
∴ Q
It's raining or snowing. It's not raining. ∴ It's snowing.