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!

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”

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

Quiz!

Prove that the following two claims are equivalent using a truth table:

P > (Q v R) ~P v (Q v R)

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

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)

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]

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

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)]

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

Practice

Now let's practice!