NIMCET 2009 — Reasoning PYQ

1. Analyze the Main Statement:

The main statement is a conditional: "Each time Sachin is the captain, India loses."

In logical terms, this can be written as:

• If $C$, then $L$ (where $C$ = Sachin is captain, $L$ = India loses).

2. Logical Rules for Implication ($C\to L$):

A conditional statement $p\to q$ has only two logically valid inferences:

• Affirming the Antecedent (Modus Ponens): If $p$ happens, then $q$ must happen. ($p\to q$)

• Contrapositive (Modus Tollens): If $q$ does not happen, then $p$ did not happen. ($\neg q\to \neg p$)

3. Evaluate the Statements:

• ($P$): Sachin is the captain ($C$)

• ($Q$): India did not win (This is equivalent to "India loses," which is $L$)

• ($R$): Sachin is not the captain ($\neg C$)

• ($S$): India won (This is the negation of losing, which is $\neg L$)

4. Check the Options for Consistency:

• Option (a) PS: $P\to S$. If Sachin is captain, India won. This contradicts the main statement.

• Option (b) SR: $S\to R$. If India won ($\neg L$), then Sachin was not the captain ($\neg C$). This is the contrapositive ($\neg L\to \neg C$) of the original statement. It is logically consistent.

• Option (c) SP: $S\to P$. If India won, Sachin is the captain. This contradicts the main statement.

• Option (d) RP: $R\to P$. If Sachin is not the captain, then Sachin is the captain. This is logically impossible.

Note on Option (b):

The pair SR follows the rule: "If the result ($L$) did not occur, the cause ($C$) must not have been present." Since India won ($S$), it implies Sachin was not the captain ($R$).

Final Answer:

The logically consistent ordered pair is SR.

Correct Option: (b)