Introductory Logic Test #2 October 21, 2005 Name: ________________________ R. Hammack Score: _________

1.
(20 points) Translate the following sentences into symbolic form. Use capital letters to represent simple statements. For each letter you use, please indicate what statement it stands for (e.g. N = "my nose itches").

 (a) If Harriet Miers is nominated to the Supreme Court, then Democrats will object and Republicans will too.

 (b) If you did poorly on the first test, the grade will be dropped if you do well on the second.

 (c) Cigarette manufacturers are neither honest nor socially responsible.

 (d) You get credit for a course if and only if you take it and you pass it.

 (e) Either the train is on time or the train is late.

2.
(20 points) Write out the truth tables for the following propositions. For each proposition, say if it is tautologous, self-contradictory, or contingent.

 (a) ( S ⊃ R ) • ( S • ~ R )

 (b) ( ~ K ⊃ H ) ≡ ( H ∨ K )

3. (20 points) Determine if the following pairs of statements are logically equivalent, contradictory, consistent, or inconsistent.

 (a) ~ ( B ∨ A ) ~ B • ~ A

 (b) ~ A ≡ X ~ ( ~ A ∨ X ) ∨ ( A • ~ X )

4. (20 points) Use indirect truth tables to decide if the following sets of statements are consistent or inconsistent.

 (a) K ≡ ( R ∨ M ) K • ~ R M ⊃ ~ K

 (b) ( N ∨ C ) ≡ E N ⊃ ~ ( C ∨ H ) H ⊃ E C ⊃ H

5. (20 points) Use any technique from Chapter 6 to decide if the following arguments are valid or invalid.

 (a) If high school graduates are deficient in reading, then they will not be able to compete in the modern world. If high school graduates are deficient in writing, then they will not be able to compete in the modern world. Therefore if high school graduates are deficient in reading, then they are deficient in writing.

(b)
 G ⊃ H H ⊃ I ~J ⊃ G ~I J