January 13, 2006
|(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.|
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.|