Final answer:
The statement that follows from S1 and S2 using logical inference is C: If a person is kind, he is not known to be corrupt. This is derived using the modus tollens inference rule, avoiding fallacies such as affirming the consequent or denying the antecedent.
Step-by-step explanation:
The question asks which statement logically follows from two given statements S1 and S2 using sound inference rules of logic. These statements are:
- S1: If a candidate is known to be corrupt, then he will not be elected.
- S2: If a candidate is kind, he will be elected.
Using logical inference rules, we can analyze these statements. Looking at S1, we know that being corrupt is a sufficient condition for not being elected, whereas S2 tells us that being kind is a sufficient condition for being elected. The question presents four possible statements that could follow from S1 and S2, and we have to determine which one is logically correct.
The correct statement that follows is:
C. If a person is kind, he is not known to be corrupt.
This is an example of a modus tollens inference. Based on S2, if a person is kind and therefore will be elected, it logically implies (by S1) that he cannot be corrupt, because if he were known to be corrupt, S1 states he would not be elected. Therefore, if a candidate is elected (because he is kind), he cannot be known to be corrupt.
It's important to avoid logical fallacies like affirming the consequent or denying the antecedent, which could lead to incorrect conclusions.