Introductory Logic Test #2 January 13, 2006 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) A day is a test day for Logic if and only if the day is a Friday and the month is January.

 (b) I will give you a make-up test only if you request it.

 (c) If Internet use continues to grow, then more people will become cyberaddicts, and normal human relations will deteriorate.

 (d) We will have a picnic unless it rains.

 (e) If you hold down the shift key and press the delete button, then your computer will explode, and you'll have to buy a new one and rewrite all your files.

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) ~ ( X ⊃ Y ) Y ∨ ~ X

 (b) A ∨ ( B • C ) ( A ∨ B ) • ( A ∨ C )

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

 (a) K ≡ ( A • ~P ) A ⊃ ( P • ~S ) S ⊃ ~ K A • ~K

 (b) ( Q ∨ K ) ⊃ C ( C • P ) ⊃ ( N ∨ L ) C ⊃ ( P • ~L ) Q • ~N

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

 (a) Elvis was a space alien or he was not a hound dog. If Elvis was a space alien, then he's still alive. Thus, if Elvis was a hound dog, then he's still alive.

(b)
 J ⊃ (~L ⊃ ~K) K ⊃ (~L ⊃ M) (L ∨ M) ⊃ N J ⊃ N