Question

Given the following premises:

1) N ⊃ ∼(S ∨ K)
2) S ∨ K
3) S ⊃ (R • Q)
Group of answer choices
A) S 2, Simp
B) (S ∨ K) ∨ N 2, Add
C) ∼S ⊃ K 2, Impl
D) ∼N 1, 2, MT
E) (S ⊃ R) ⊃ Q 3, Exp

Answer 1

The correct answer to the student's logical reasoning question is D) ¬N, which is derived using Modus Tollens. The student is applying rules of inference to evaluate premises and derive a logical conclusion within the field of mathematics.

Step-by-step explanation:

The student is working with logical reasoning within the scope of formal logic, a branch of mathematics. Logical reasoning involves various logical forms and inference patterns, such as disjunctive syllogism, modus ponens, and modus tollens. Let's examine the premises provided:

1. N ⊃ ¬(S ∨ K)
2. S ∨ K
3. S ⊃ (R • Q)

Given these premises, we can use the provided rules of inference to derive a conclusion. The correct answer is D) ¬N using Modus Tollens (MT). Here's the step-by-step explanation:

• From premise 1 (N ⊃ ¬(S ∨ K)), we understand that if N is true, then neither S nor K can be true (¬(S ∨ K)).
• Premise 2 (S ∨ K) informs us that either S or K is true.
• Given that the negation (¬(S ∨ K)) of the previous statement is the consequent in the first premise, by Modus Tollens, we infer that N cannot be true (hence, ¬N).

Therefore, the correct conclusion drawn from these premises is ¬N, which means N is not true.