Explanation
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:
2. Logical Rules for Implication (C→L):
A conditional statement p→q has only two logically valid inferences:
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Affirming the Antecedent (Modus Ponens): If p happens, then q must happen. (p→q)
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Contrapositive (Modus Tollens): If q does not happen, then p did not happen. (¬q→¬p)
3. Evaluate the Statements:
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(P): Sachin is the captain (C)
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(Q): India did not win (This is equivalent to "India loses," which is L)
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(R): Sachin is not the captain (¬C)
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(S): India won (This is the negation of losing, which is ¬L)
4. Check the Options for Consistency:
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Option (a) PS: P→S. If Sachin is captain, India won. This contradicts the main statement.
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Option (b) SR: S→R. If India won (¬L), then Sachin was not the captain (¬C). This is the contrapositive (¬L→¬C) of the original statement. It is logically consistent.
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Option (c) SP: S→P. If India won, Sachin is the captain. This contradicts the main statement.
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Option (d) RP: R→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)
