Philosophy 251: Handout #3

III. Which of the following are formulas of SL and which are not? For those that are not explain why not.

1. B & Z	6. &
2. & H	7. ( I v [ T E ] )
3. ~~O	8. [ U & C & ~L ]
4. M ~ N	9. ( F K ) [ M v K ]
5. J( K( A v N ) )	10. [( G v E ) ( ~H & ( K v B ) ]

IV. For each of the following formulas determine whether it has the same form as:

(a) ~ ( v )

(b) ~( )

(c)

Eg 1. P~( Q v T )

Answer: (a) No. (b) No. (c) Yes.

Eg 2. ~( Q & P ) v ( Q T )

Answer: (a) No. (b) No. (c) No.

1. ~P ( Q & ( R v T ))	6. ~( P T ) v ( P T )
2. Q & ~( R T )	7. ~[ ~P ( Q v S )]
3. ~( P & Q ) ( R v T )	8. ( ~S T ) ~( S & T )
4. ~[(P & Q ) T ]	9. ~~ [(P v T ) ( T v P )]
5. ~~P ( ~Q v ~S )	10. ~[ W ( Q & S )] [(P & T ) v ( R Q )]

V. Translate the following sentences into formulas of SL.

1. Bob and Carol jog regularly.
2. Bob is a regular jogger, but David isn't.
3. Albert jogs regularly and so does Carol, but Bob doesn't.
4. Al and Bob are democrats.
5. Carol is not a rich lawyer.
6. Carol or David votes republican, but not both.
7. Although Al is a staunch democrat, he still likes David and Carol.
8. Either Bob jogs regularly or Carol is a democrat or David doesn't jog regularly.
9. Bob, David, and Al are all roommates.
10. David and Carol are getting married, but not to each other.
11. Neither Carol nor David jog with the president.
12. It is not the case that David or Al protect the president, but Bob does.
13. Bob, David, Carol, and Al all work for the Secret Service.
14. Bob jogs with the president, but either David or Al works in the counterfeit division.
15. Carol and Bob are well-respected agents, but neither is a spy.