Question

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

Given the following premises:
1. N ≡ R
2. (N • ∼R) ⊃ C
3. N
Group of answer choices
a. R 1, 3, MP
b. N • (∼R ⊃ C) 2, Assoc
c. (N ⊃ R) ∨ (R ⊃ N) 1, Equiv
d. C ⊃ (N • ∼R) 2, Com
e. N ⊃ (∼R ⊃ C) 2, Exp

Answer 1

Option (a) R is the correct conclusion, derived from premises 1 and 3 using modus ponens, a form of deductive reasoning.

Step-by-step explanation:

The question involves identifying the valid conclusion derived from a set of given premises using the rules of deductive reasoning and logical inference. We are provided with three premises: N ≡ R (1), (N • ∼R) ⊃ C (2), and N (3). The correct conclusion that can be drawn in a single step from these premises is option (a) R, which is derived using modus ponens. Modus ponens is a form of deductive reasoning where if a conditional statement (P ⟶ Q) and its antecedent (P) are given to be true, then the consequent (Q) follows. In this case, premise 1 (N ≡ R) can be read as N implies R and since premise 3 asserts that N is true, we conclude that R is also true.