General Directions. There are four (4) sections to this exam. Please read and fo

Question

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.

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.

Explanation / Answer

ANSWER 1

-> For conditions

~ for negotiation

v for disjunction

& for conjunction

<-> for biconditional

/ for conlusion

1. C -> R

2. C & R-> B

3. R -> B <-> ~S

4. S v T

5. C & R

6. T

7. /

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