Question 1 - 6 points each

A) Derive D v W from {(A v B) ⊃D, C ⊃E, A & C}.

B) Derive B ⊃(A & ~A) from {(B ⊃~A) & (B ⊃A)}.

C) Derive K ≡ (M & S) from {K ⊃M, M ⊃(S & K)}.

D) Derive ~A from {A ⊃(~B & ~C), (~B v ~D) ⊃F, F ⊃~A}. E) Derive K ⊃N from {H ⊃J, (~H v J) ⊃(K ⊃N)}

Q2 –Provide derivations which show the following. 8 points each

A) ~B is derivable from {B⊃~C, (~A v C) , A}.

B) {~(AvD), ~A⊃B, ~B&C} is inconsistent.

C) (A⊃~B)&C is equivalent to C&(~B v ~A).

D) (Q v R) ⊃ [(Q v S) v (R v P)] is a theorem of SD.

E) The following argument is valid:

1. A≡(C⊃B) 2. ~C ------------------ 3. B⊃A

Question 3 - 6 points each

A) Suppose that X is derivable from {Y}. Does it follow that (X v Z) is derivable from {Y}? Explain, with reference to particular rules in SD. (Note that “X”, “Y”, and “Z” are variables here, so could stand for any sentence in SL, including complex ones).

B) Suppose that X is equivalent to Y. Does it follow that we can derive Z, from {X&~Y}? Explain, with reference to particular rules is SD. (Note that “X”, “Y”, and “Z” are variables here, so could stand for any sentence in SL, including complex ones).

C) Suppose that X is derivable from {Y}. Does it follow that Y ⊃X is a theorem? Explain, with reference to particular rules in SD. (Note that “X” and “Y” are variables here, so could stand for any sentence in SL, including complex ones).

Subject | Philosophy |

Due By (Pacific Time) | 04/17/2015 08:00 am |

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