Test

Phil & 120

Practice Exam 4

Section I:  Translate into Predicate Logic. Use the letters provided.

(1) Mark is either a philosopher or a lawyer. (P, L)

(2) All things are good. (G)

(3) Every Vulcan is logical. (V, L)

(4) Some politicians are not corrupt. (P, C)

(5) Some dogs are pets. (D, P)

Section II: Predicate Logic Proof Construction. Show all your work.

6.  Find:  (x)(Tx ⊃ Wx)                                9.  Find:  (∃y)Cy

       1.  (x)(Tx ⊃ Mx)                                                       1.  (x)[(Ax v Bx) ⊃ Cx]

       2.  (x)(Mx ⊃ Wx)                                        2.  (∃y)(Ay • Dy)

7.  Find:  Bz • Bv                                        10. Find: (x)Bx                        

       1.  (x)(Ax ⊃ Bx)                                              1. (x)(Ax ∙ Bx) v (x)(Cx ∙ Dx)

       2.  Az • Bv                                              2. ~(x)Dx

8.  Find:  (∃x)Bx                                        11. Find: (x)Cx ⊃ (∃x)~Ax

       1.  (x)[Ax ⊃ (Bx v Cx)                                      1. (x)Ax ⊃ (∃x)~Bx

       2.  (∃x)(Ax • ~Cx)                                      2. ~(x)Bx ⊃ (∃x)~Cx

12. Find: (x)Cx

                                                              1. (∃x)~Ax ⊃ (x)~Bx

                                                              2. (∃x)~Ax ⊃ (∃x)Bx                                                                                            3. (x)(Ax ⊃ Cx)

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