Int To Logic

Question Description

Question# 1

Part A:

Come up with aninstance of argument that conforms to HS.

 Derive theconclusion from the given premises in the argument below by utilizing the rulesof inference (hint: use HS, MT, DS, or some other combination, as analternative is available here).

         C:   B

      ==================

        P1:   A  V  B

        P2:   C ⊃  D

        P3:   A ⊃  C

        P4:  ~D

      ========================================================================

Part B:

Exercise 31

Do a Proof for thefollowing argument: Use TT for testing validity. Follow thethree steps:

 1. Assign P, Q, and R to the atomic sentences in the order of appearancein the argument.

 2. Formalize the argument.

 3. Derive the conclusion from the premises by using the rules of inference.

     P1:  If things are caused to exist, then the infinite regress of existenceis not possible.

     P2:  God is not the ultimate cause of existence, only if the infiniteregress of existence is possible.

     P3:  By the way, things are caused to exist.

     C:   Therefore, God is the ultimate cause of existence.

[31-2]”Derive” the conclusion (C) from the 3 premises (1 to 3) in aformalized argument below by employing rules of inference (i.e., proof, whereyou need to come up with additional steps beyond 3 below to lead you to theconclusion):

        C.  ~T

        —————————–

        1.  (R V S) ⊃ (T ⊃ K)

        2.  ~K

        3.  R V S

        —————————–

Part C:
Determine whether the following argument is valid or not
by showing how truth tables are utilized and interpreted:

[26-1]  P1:  P -> Q

 P2:  Q -> R

  P3: ~R

      ————————-
        C:  ~P

[26-2]  P1:  ~D  V ~F

      P2:  G-> (D & F)

    —————————–

   C:  ~G 

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