Question

Given the following premises:

1. ∼∼N
2. K ⊃ ∼N
3. ∼N ∨ (K • S)
a) (∼N • K) v (∼N • S) 3, Dist
b) (∼N v K) • S 3,Assoc
c) K 1,2,MT
d) K • S 1,3,DS
e) N ⊃ ∼ K 2,Trans

Answer 1

The question revolves around validating logical inferences through forms like disjunctive syllogism, modus ponens, and modus tollens based on given premises and within the context of necessary and sufficient conditions.

Step-by-step explanation:

The question is asking to validate logical form and inferences based on given premises. This involves understanding forms such as disjunctive syllogism, modus ponens, and modus tollens. These forms rely on the relationships between necessary and sufficient conditions to draw valid conclusions from the premises provided. For instance, modus ponens infers that if 'X is sufficient for Y' (P > Q), and 'X is true' (Q), then 'Y must be true' (P). Similarly, modus tollens states that if 'Y is necessary for X', and 'Y is not true', then 'X is also false'. It is crucial to ensure that the premises do not contain logical fallacies such as circular reasoning or false lemmas, as these would invalidate the argument.