Valid Forms

Disjunctive Syllogism

A valid argument form using an 'either … or' statement that eliminates one option to affirm the other.

Structure:

• Premise 1: Either P or Q

• Premise 2: Not P

• Conclusion: Therefore, Q

Hypothetical Syllogism

A chain of reasoning using conditional statements in the form 'if … then,' leading to a conclusion based on premises.

Structure:

• Premise 1: If P, then Q

• Premise 2: If Q, then R

• Conclusion: Therefore, if P, then R

Modus Ponens

A valid argument form where if a conditional statement is true and its antecedent is affirmed, then the consequent must also be true.

Structure:

• Premise 1: If P, then Q

• Premise 2: P

• Conclusion: Therefore, Q

Modus Tollens

A valid argument form where if a conditional statement is true and its consequent is denied, then the antecedent must also be false.

Structure:

• Premise 1: If P, then Q

• Premise 2: Not Q

• Conclusion: Therefore, not P