Module Complete
Validity & Proofs — Quick Reference
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Completion
Inference Rules
Modus Ponens
P→Q, P ∴ Q
Modus Tollens
P→Q, ¬Q ∴ ¬P
Hypothetical Syllogism
P→Q, Q→R ∴ P→R
Disjunctive Syllogism
P∨Q, ¬P ∴ Q
Common Fallacies
Affirming the Consequent
P→Q, Q ∴ P — INVALID
Just because Q is true doesn't mean P caused it.
Denying the Antecedent
P→Q, ¬P ∴ ¬Q — INVALID
Q could be true for other reasons.
Key Takeaways
1
Valid = if premises true, conclusion MUST be true
2
Modus Ponens and Tollens are your core tools
3
Affirming consequent and denying antecedent are traps
4
Build proofs step-by-step with clear justifications
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Up Next
Module 4: Predicate Logic
Quantifiers, relations, and structure