Logic / Unit 5 Logic 201 worked example, 60 to 90 seconds
First Proof Walkthrough
The idea
A natural deduction proof reaches the conclusion one line at a time, and every line carries a justification naming the rule applied and the earlier lines it draws on.
In practice
Two premises. Line one: A horseshoe B. Line two: A dot C. The goal is B dot C. Line three: A, from line two by simplification — a conjunction licenses either half on its own. Line four: B, from lines one and three by modus ponens, since a conditional together with its antecedent delivers its consequent. Line five: C, from line two by simplification again, taking the other half this time. Line six: B dot C, from lines four and five by conjunction, which permits two established lines to be joined. Four moves and the proof is complete. Write each justification before attempting the next line, not afterwards. A line without its justification cannot be checked by anyone, including the person who wrote it an hour later.
Where people slip
Simplification applies to a line whose main connective is the dot, and to nothing else. Used on a conditional or a disjunction it produces a line that looks derived and rests on air. Name the main connective first, then choose the rule that attaches to it.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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