LESSON 4 – PRACTICE EXERCISE KEYNOTE – Any homework exercises for this lesson not included below are gradeable by the software program and/or through the online Grade Grinder2.1 Valid Sound in Socr Sound in Wit1 V S U2 V S U3 V S U4 V S U5 I U U6 V S U7 I U U8 I U U2.2 (there may be other legitimate ways to interpret these arguments)1. Anyone who wins an AW is famousMeryl St won an AW---- (Therefore,) Meryl St is famous.VALID / SOUND?? – DEPENDS ON HOW YOU DEFINE “FAMOUS”2. Actors who win AW are famousHarr Ford has never won an AW---- Harr Ford is not famous.INVALID / UNSOUND3. CH said the right to bear arms is the most important freedom.CH is never wrong.---- The right to bear arms is the most important freedom.VALID / UNSOUND4. Al Gore is a politician Hardly any politicians are honest---- Al Gore must be dishonestINVALID / UNSOUND5. Sam Clemens was born in Hannibal, MOMark Twain is Sam Clemens---- Mark Twain lived in Hannibal, MOINVALID / UNSOUND6. We were closed last nightNo one under 21 bought beer here last night---- No one bought anything last night.VALID7. Max lives on the same street as Laura.Claire lives on the same street as Max---- Claire lives on the same street as LauraVALID2.3 (Again, there may be other ways to interpret these …)1. Many of the students in the film class atend film screenings.--- There must be many students in the film class.INVALID – DIFFERENT SCOPES OF “MANY” HERE2. There few students in the film classMany of these students atend the film screenings---- There are many students in the film classINVALID3. Many students atend film screeningsOnly students in the film class atend screenings---- There are many students in the film classVALID4. There are thirty students in the film classSome of the students turn in their homework on timeMost of the students went to the all-night party---- Some student who went to the party managed to turn in the homework on timeINVALID5. There are thirty students in my logic classSome of the students turned in their homework on timeThey all went to the party---- Some student who went to the all-night party must have turned in the homework on timeVALID (THOUGH AMBIGUOUS-BUT VALID ON EITHER INTERPRETATION OF “THEY”)6. There are thirty students in my logic classMost of the students turned in their homework on timeMost of the students went to the all-night party---- Some student who went to the party turned in the homework on timeVALID2.5 We are told that a = b and also that b = c. Using the later identity statement (b = c), by the indiscernibility of identicals we may substitute c for b in the first identity statement (a = b), giving us a = c. Thus, we have proven the transitivity of identity.2.7 a) Yes.b) NO. Not only might Nancy not be Claire’s mother, Nancy might not be a nybody’s mother.c) NO. Claire might be Nancy’s sister and Max’s aunt.THE FOLLOWING ARGUMENTS ARE VALID:*2.9 We are told that a is left of b and that b = c; therefore, by the indiscernibility of identicals, a must be left of c. But if a is left of c, then c must be right of a, because “right of” and “left of” are inverses of one another.2.12 We are told that a is in back of b; therefore, b must be in front of a, because “in back of” and “in front of” are inverse relations. We are also told that a is in front of c; therefore, b must be in front of c by the transitivity of “in front of.”2.13 We are told that a is larger than c; therefore, c is smaller than a by the fact that “is larger than” and “is smaller than” are inverse relations. We are also told that a is the same size as b; therefore, c is smaller than b because of the fact that “Is the same size as” is a symmetric relation. We are told that d is smallerthan c; therefore d is smaller than b because “is smaller than” is a transitive relation.2.14 We are told that a is to the left of c, but we are also told that b is between a and c. Therefore, by the meaning of the predicate “between,” b must be both to the right of a and to the left of c. But if b is to the right of a, then it a is also to the left of b, because “right of” and “left of” are inverses of one another.*NOTE THAT YOU SHOULD BE ABLE TO BUILD COUNTEREXAMPLE WORLDS IN TARSKI’S WORLD FOR EXERCISES 2.8, 2.10, AND 2.11 BECAUSE THOSE ARGUMENTS ARE INVA
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