Question

Select the conclusion that follows in a single step from the given premises.

Given the following premises:
1. (E ⊃ K) ∨ ~W
2. ∼W
3. W ∨ (Q ⊃ E)
a. Q ⊃ E 3, Simp
b. E ⊃ K 1, 2, DS
c. Q ⊃ K 1, 3, HS
d. Q ⊃ E 2, 3, DS

Answer 1

The correct conclusion derived from the given premises using disjunctive syllogism is (b) E ⊃ K.

Step-by-step explanation:

The student is tasked with selecting a single-step conclusion from a set of given premises using logical deductive reasoning. In reviewing the premises:

1. (E ⊃ K) ∨ ~W
2. ~W
3. W ∨ (Q ⊃ E)

We can apply a disjunctive syllogism to derive a conclusion from premises 1 and 2. The disjunctive syllogism uses the following logical form:

1. X or Y
2. Not Y
3. Therefore X

Given the second premise is ~W (Not W), and the first premise offers a disjunction that includes ~W, we conclude that E ⊃ K (if E then K) must be true. Reflecting this deduction on the answer choices given, answer choice (b) E ⊃ K is the correct conclusion derived in a single step using disjunctive syllogism (1, 2, DS).