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Quiz, Last Rules

Quiz, Last Rules. Sign In! Last Day!!! :( HW Due Quiz! EXP, ASSOC, DIST, TAUT For Next Time: Study for the final!. Quiz!. What is the name of the following logical operator? Create a truth table for the claim in which it appears A v ~B. Quiz!.

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Quiz, Last Rules

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  1. Quiz, Last Rules • Sign In! • Last Day!!! :( • HW Due • Quiz! • EXP, ASSOC, DIST, TAUT • For Next Time: • Study for the final!

  2. Quiz! • What is the name of the following logical operator? Create a truth table for the claim in which it appears • A v ~B

  3. Quiz! • Translate the following sentence into standard sentential logic notation: • “It is not the case that if the final will be hard then very few people will do well on it”

  4. Quiz! • Prove whether the following argument is valid or invalid using a short truth table: • 1. A > (B & C) • 2. B > ~(H) • 3. :. H > A

  5. Quiz! • Prove that the following two claims are equivalent using a truth table: • P > (Q v R) • ~P v (Q v R)

  6. Quiz! • Use any of the rules on page 333 to solve the following derivation: • 1. (A v B) > C • 2. H > ~C • 3. A / :. ~H

  7. Quick Review • Today we finish reviewing all of the rules for derivation • We have already covered most of these rules • Remember that there will often be several different ways of deriving a claim using premises • This is because the rules are all telling us things we already know from truth tables: • 1. (P > Q) = (~P v Q) = (~Q > ~P)

  8. Exportation (EXP) • Exportation is another equivalence rule • Exportation tells us that if we have a conditional that implies another conditional that we can turn this into another conditional • The new conditional will have the antecedents of the two original conditionals as a conjunction • [P > (Q > R)] = [ ( P & Q) > R] • Exportation holds even for complex conditionals • [(P v Q) > (R > S)] = [ [(P v Q) & R] > S]

  9. Association (ASSOC) • Association is a distribution rule that lets us distribute conjunctions or distributions • [P & (Q & R)] = [(P & Q) & R] • Conjunctions are only true when both conjuncts are true, when we have three claim variables and two conjunctions this means all variables are true • [P v (Q v R)] = [(P v Q) v R] • Disjunctions are true when either disjunct is true, with three claim variables and two disjunctions, at least one of the claim variables will be true

  10. Distribution (DIST) • Another replacement rule. Distribution applies only in cases with three claims joined by conjunctions and disjunctions • [P & (Q v R)] = [( P & Q) v (P & R)] • If a conjunction is true then we know both conjuncts are true. If the disjunction is true then at least one disjunct is true. This is all DIST tells us • [P v (Q & R)] = [(P v Q) & (P v R)]

  11. Tautology (TAUT) • The tautology rule is perhaps the simplest of all the rules • It is also the last rule we will look at • P v P = P • P & P = P • All it does is let us derive a claim when the same claim is on both sides of a conjunction or disjunction

  12. Practice • Now let's practice!

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