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


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