Question

Select the conclusion that follows in a single step from the given premises. Throughout this test, write your answer on the form provided. Erasure marks may cause the grading machine to mark your answer wrong.

Given the following premises:
1. T ∨ S
2. A ⊃ T
3. A • (∼T • S)
a. T 2, 3, MP
b. (A • ∼T) • S 3, Assoc
c. ∼T 3, Simp
d. S 1, 3, DS
e. T ⊃ A 2, Com

Answer 1

Using disjunctive syllogism, we can deduce that if we have a disjunction (T or S) and one part (not T) is negated, then S must be true. Hence, the correct answer is d. S 1, 3, DS.

Step-by-step explanation:

The question from the student is asking us to identify the conclusion that follows in a single step from the given premises. The premises provided are:

1. T ∨ S (T or S)
2. A ⊕ T (If A then T)
3. A • (¬T • S) (A and not T and S)

Based on the provided premises and rules of logical inference, we can determine the correct conclusion. The correct answer to the question is d. S 1, 3, DS. This is because using the rule of disjunctive syllogism (DS), we can deduce that if we have a disjunction (T or S) and we know that one part of the disjunction cannot be true (not T, as from the third premise), S must be true.