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Question

Consider the following arguments.

S1:{(ABC),(B(AC))}B

S2:{B(PR),RB,PR}

Which of the following is true?

A
S1 is not valid and S2 is valid
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B
Neither S1 not S2 is valid
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C
Both S1 and S2 are valid
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D
S1 is valid and S2 is not valid
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Solution

The correct option is A S1 is not valid and S2 is valid
option(b)

S1:{(ABC),(B(AC))}B

When A is true, B is false and C is true, then all the premises have truth value true and the conclusion has truth value false.
The argument S1 is not valid.
S2:{B(PR),RB,PR}

Indirect proof:

1.B(PR)Premise2.RBPremise3.PRPremise4.RNew premise to apply indirect proof5.P(3),(4),modus tollesns6.B(2),(4),modusponens7.(PR)(1),(6),modus ponens8.RP(7),simplification9.P(4),(8),modus ponens

(5) and (9) contradict each other.

The argument is valid.

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