Question

For S⊃T / S⊃~T / ~T⊃S // S v ~T, what is the valid conclusion?

A) S ⊃ T
B) ~T ⊃ S
C) S v ~T
D) ~T

Answer 1

The valid conclusion from the logical premises provided is C) S v ~T. This is concluded using the rule of Disjunctive Syllogism and considering the contradictory nature of the first two premises, which prevent a deterministic conclusion if S is assumed true. However, given the third premise, it supports the disjunction that either S or not T must be true.

Step-by-step explanation:

The student's question involves determining the valid conclusion from a set of logical premises using deductive reasoning. The premises provided are:

• S ⊃ T (If S then T)
• S ⊃ ~T (If S then not T)
• ~T ⊃ S (If not T then S)

The conclusion to be validated is S v ~T (S or not T). According to the rule of Disjunctive Syllogism, we can deduce the following:

1. We have a disjunction: S v ~T.
2. From the second premise, we can consider the case if S were true, then T would have to be false due to the presence of the contradictory premises S ⊃ T and S ⊃ ~T. This renders the premises inconsistent because the same antecedent leads to contradictory consequents, showing no deterministic conclusion can be made when assuming S is true.
3. On the other hand, if we assume ~T (not T) is true based on the third premise, then S must be true. Thus, in the event T is not true, S must hold true, supporting the claim that at least one of S or ~T is indeed true.

Given the contradicting premises, it's impossible to conclude definitively A) S ⊃ T, or B) ~T ⊃ S. However, C) S v ~T remains a logical disjunction that holds true since, given premise (3), if ~T is true, then S is true, which validates the disjunction. Therefore, the valid conclusion is C) S v ~T.