Deck 5: Proofs With CP or IP

Question 1

General Theory

-Suppose you know that a particular two-premise argument is invalid. Now suppose we add the negation of the conclusion of the two premises to form a three-sentence set of premises. Can a contradiction be derived from this three-sentence set of premises? (Defend your answer.)

Answer 1

No, because derivation of a contradiction would constitute an indirect proof of validity for the argument, but by the hypothesis of the problem, the argument in question is invalid.

Question 2

General Theory

-a. Use $\textbf{ IP }$ to prove that the following argument is valid.
b. To illustrate how indirect proofs are a kind of shortened conditional proof, cross out the last line in the above proof and complete it as a conditional proof. (Hint: as an intermediate step prove .)

Answer 2

Question 3

Proofs with CP or IP
Prove valid, using the eighteen valid argument forms and CP or IP:
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Answer 3

Question 4

Proofs with CP or IP
Prove valid, using the eighteen valid argument forms and CP or IP:

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Question 5

Proofs with CP or IP
Prove valid, using the eighteen valid argument forms and CP or IP:
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Question 6

Proofs with CP or IP
Prove valid, using the eighteen valid argument forms and CP or IP:
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Question 7

Proofs with CP or IP
Prove valid, using the eighteen valid argument forms and CP or IP:
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Question 8

Proofs with CP or IP
Prove valid, using the eighteen valid argument forms and CP or IP:
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Question 9

Show that premises in the following arguments are inconsistent:

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Question 10

Show that premises in the following arguments are inconsistent:

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Question 11

Show that premises in the following arguments are inconsistent:
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Question 12

Show that premises in the following arguments are inconsistent:

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