Subject Philosophy Logic

Question

[31-1]   Do the following 3 things to do a Proof for the following argument:
NB: This is the same argument that you worked on in Exercise 27 to use Truth Table 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. 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
-----------------------------

[33-1]   Come up with an instance of argument that conforms to HS.

[33-2]   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
-------------------
1:   A V B
2:   C -> D
3:   A -> C
4: ~D
-------------------

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Exercise 31.
1)
P ⊃ q
q ⊃ r
P ⊃ r...

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