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Logic(philosophy)

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General Directions. There are four (4) sections to this exam. Please read and follow all directions carefully. Please do not send your answers in an attachment. Note that ‘->’ is used for conditionals, ‘~’ is used for negations, ‘v’ is used for disjunctions, ‘&’ is used for conjunctions, ‘<->’ is used for biconditionals, and ‘/’ is used as the conclusion indicator.

Your answers are due no later than 9am, Friday, March 13, 2015.

A. Directions. 1. Translate the following argument into symbolic notation using the translation dictionary provided at the end of this paragraph. 2. Prove that the argument is valid using the method of Natural Deduction as outlined in Chapter 7 of Hurley’s A Concise Introduction to Logic, 12th edition. Do not use Conditional Proof (CP) in this proof. [Trans. Dict.: B = the bridge will wash out; C = the rain will continue; R = the river will rise; S = a single road is sufficient for the town; T = the traffic engineers have made a mistake. ]

If rain continues, then the river will rise. If the rain continues and the river rises, then the bridge will wash out. If the continuation of rain implies the bridge washing out, then a single road is not sufficient for the town. Either a single road is sufficient for the town or the traffic engineers have made a mistake. The rain will continue and the river will rise. Hence, the traffic engineers have made a mistake.

B. Directions. Prove the following four (4) arguments to be valid using the method of Natural Deduction. Do notuse Rule of Conditional Proof in these proofs.

B.1.

1. S v (L & D)

2. ~(~S -> T) / L

B.2.

1. (I -> O) -> G

2. ~I / (G v ~D)

B.3.

1. (G <-> E)

2. (~E v E) -> (T -> W)

3. (W -> E) / (T -> E)

C. Directions. Show the following two (2) arguments to be valid using Conditional Proof in the method of Natural Deduction, as Hurley outlines it in Chapter 7.

C.1.

1. (H v H) -> [(B -> S) & (L -> S)]

2. D -> (B v L) / D -> (H -> S)

C.2.

1. [J -> (T & L)]

2. [P -> (R & M) / [(L -> P) -> (J -> M)]

D. Directions. There are 5 statements below, in English. Translate these statements into symbolic notation using the following translation dictionary: A = AT&T will pay increased Federal taxes; C = Monsanto’s CEO will step down; D = Dupont will pay increased Federal taxes; G = General Motors will pay increased Federal taxes; M = Monsanto is facing financial ruin;

1. Monsanto will face financial ruin only if its CEO will step down.

2. Either the CEO will step down or neither AT&T nor Dupont will pay increased Federal taxes.

3. AT&T won’t pay more taxes but Monsanto’s CEO won’t step down.

4. Dupont not paying more taxes is not a necessary condition for Monsanto facing financial ruin.

5. Dupont and General Motors not paying increased taxes is a sufficient condition for Monsanto’s CEO to not step down.

End of exam #3

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