Project #67080 - Sentential Logic Derivations Assignment

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(CB) 2. ~C ------------------ 3. BA

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 Zare 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 Zare 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 Xand Yare 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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