Question

Consider the following two statements:
$S_1$:If a candidate is known to be corrupt, then he will not be elected .
$S_2$: If a candidate is kind, he will be elected .
Which one of the following statements follows from $S_1$ and $S_2$ as per sound inference rules of logic?

• A. If a person is known to be corrupt, he is kind
• B. If a person is not known to be corrupt, he is not kind
• C. If a person is kind, he is not known to be corrupt
• D. If a person is not kind, he is not known to be corrupt

Answer 1

The correct option is C If a person is kind, he is not known to be corrupt

C : Person is corrupt
K: Person is kind .
E: Person is elected
$S_1:C\to \overline{E}$
$S_2:K\to E$
$S_2\cong \overline{E}\to \overline{K}$
So from$S_1$ and $S_2$: $(C\to \overline{E})\wedge \overline{E}\to \overline{K})\cong C\to \overline{K}$
We can conclude C $\to \overline{K}$ which is same as K $\to \overline{C}$, which is same as option (c).