GATE CS 2015 Set 2 Q3 — Propositional and First Order Logic

Let us define the following propositional variables for a candidate:

• $C$: The candidate is known to be corrupt.
• $E$: The candidate is elected.
• $K$: The candidate is kind.

We can translate the given statements $S_1$ and $S_2$ into logical implications:

• $S_1$: If a candidate is known to be corrupt, then he will not be elected.
  $$C \implies \neg E$$
• $S_2$: If a candidate is kind, he will be elected.
  $$K \implies E$$

Using the law of contrapositive, $S_1$ can be rewritten as:

Now, applying the rule of hypothetical syllogism (transitivity of implication) to $S_2$ and the contrapositive of $S_1$:

Translating the inferred statement $K \implies \neg C$ back into English:

"If a person is kind, then he is not known to be corrupt."

This corresponds to Option C.