Int. to Logic

/in /by

Question# 1

Part A:

Come up with an instance of argument that conforms to HS.

Derive the conclusion from the given premises in the argument below by utilizing the rules of inference (hint: use HS, MT, DS, or some other combination, as an alternative is available here).

C:   B

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

P1:   A  V  B

P2:   C ⊃  D

P3:   A ⊃  C

P4:  ~D

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Part B:

Exercise 31

Do a Proof for the following argument: Use TT for testing validity. Follow the three steps:

1. Assign P, Q, and R to the atomic sentences in the order of appearance in 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 existence is not possible.

P2:  God is not the ultimate cause of existence, only if the infinite regress 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 a formalized argument below by employing rules of inference (i.e., proof, where you need to come up with additional steps beyond 3 below to lead you to the conclusion):

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