GATE DA 2026 Set 1 — Question 38

The given sentence is: "Assume that a Creative ($C$) person will Succeed ($S$) if the person is also Disciplined ($D$), but will not succeed otherwise."This can be translated into logical implications for a person who is Creative ($C$):Combining these under the condition of being Creative ($C$):
$C \Rightarrow (D \Rightarrow S)$ and $C \Rightarrow (\neg D \Rightarrow \neg S)$.The second part $\neg D \Rightarrow \neg S$ is the contrapositive of $S \Rightarrow D$. Thus, for a Creative person, $D \Rightarrow S$ and $S \Rightarrow D$ both hold. This means $S$ is equivalent to $D$.So, the sentence implies: $C \Rightarrow (S \Leftrightarrow D)$. This matches statement (ii).Let's check the other statements:
(i) $C \wedge S \Leftrightarrow D$: This implies that if a person is not Creative ($C$ is false), then $D$ must be false (since LHS is false). The premise does not state anything about non-creative people. Thus, (i) is not necessarily true.
(iii) $C \Leftrightarrow ((D \Rightarrow S) \vee \neg S)$: The RHS simplifies to $(\neg D \vee S) \vee \neg S \equiv \neg D \vee (S \vee \neg S) \equiv \neg D \vee \text{True} \equiv \text{True}$. This statement would imply $C \Leftrightarrow \text{True}$, meaning everyone is Creative, which is not supported by the premise.Therefore, only statement (ii) is logically valid based on the premise.