# Part I: use the 8 inference rules (Simp. Conj. D.S., H.S., DIL, M.P., M.T., Add) to prove the following arguments. You are NOT allowed to use any of the 10 replacement rules, nor C.P. or I.P.

Symbolic Logic PHIL 1150 Exam No.2 Version A. Name______________________
(Total: 30 points, 10 questions; each question is worth 3 points)
Part I: use the 8 inference rules (Simp. Conj. D.S., H.S., DIL, M.P., M.T., Add) to prove the following arguments. You are NOT allowed to use any of the 10 replacement rules, nor C.P. or I.P.
a)
1. (AvB) •(CD)
2. ~C~A
3. ~B•~D /~(PQ)
b)
1. ((PQ)v~S) •~C
2. W ((PQ) A)
3. (WvC)•(~SB) /AvB
Part II: Use 8 inference rules and 10 replacement rules (D.N., C.E., B.E., DeM., Dup., Assoc., Commu., Dist., Contrap., Export.) to prove the following arguments. You are NOT allowed to use C.P. or I.P.
c)
1. ~C ⊃(E ∙ F)
2. E ∙~(FvD)
3. (~Av~B) ⊃(~CvD) / ∴A
d)
1. (A  B)  C
2.  (C  A) B
e)
1. M  (I ≡ F)
2. K  (I ≡ D)
3. L  (I ≡S)
4. (S  T) • (F T)
5. (D • T) • I / (MvKvL)
f)
1. A ≡B
2. ~(BvW)
3. R⊃ (BvA)
4. ((PvB) ≡R) ⊃(AvW) /∴ PvQ
g)
1. J ≡ K
2. ~K≡ ~L / ∴ J ≡ L
Part III: C.P. (conditional proof), I.P. (indirect proof), and proof of theorems.

1. Use C.P. or/and I.P. to prove the following.
h)
1. (A v B) ⊃ (F• D)
2. ~(A •~ D)
3. ~F ⊃~ (C• D)
4. C v A / ∴ A≡~C
i)
1. A⊃(B⊃C)
2. (C•D)⊃E
3. F⊃~(D⊃E) /∴ A⊃(B⊃~F)
2. Prove the following theorem.
j) ((pvq) ⊃ (p•q)) ≡(p≡q)

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