in the below

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[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 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

Exercise 33 … (For-Credit of 5 points)

[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

C: B

1: A V B

2: C -> D

3: A -> C

4: ~D