Question:
Main statement: The computer will not work if operating system fails.- Operating system fails.
- Operating system does not fail.
- The computer does not work.
- The computer works.
The ordered pair of statements is:
This questions has a main statement followed by four statements: 1, 2, 3, 4. Choose the ordered pair of statements where the first statement implies the second, and the two statements are logically consistent with the main statement.
Main statement: The computer will not work if operating system fails.
This questions has a main statement followed by four statements: 1, 2, 3, 4. Choose the ordered pair of statements where the first statement implies the second, and the two statements are logically consistent with the main statement.
- Operating system fails.
- Operating system does not fail.
- The computer does not work.
- The computer works.
This questions has a main statement followed by four statements: 1, 2, 3, 4. Choose the ordered pair of statements where the first statement implies the second, and the two statements are logically consistent with the main statement.
Updated On: Jul 15, 2026
- 2, 1
- 2, 3
- 1, 4
- 4, 2
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The Correct Option is D
Approach Solution - 1
The correct option is (D): 4, 2.
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Approach Solution -2
The main statement, 'The computer will not work if operating system fails', is a conditional: operating system failure implies the computer does not work. Its logically valid flip side, the contrapositive, is: the computer working implies the operating system did not fail. Let's check each option:
- 2, 1: 'Operating system does not fail' implying 'Operating system fails' contradicts itself outright, the same condition cannot both hold and not hold. Invalid.
- 2, 3: 'Operating system does not fail' implying 'The computer does not work' is not something the main statement guarantees, the main statement only tells us what happens when the system fails, it says nothing about what happens when it does not fail, the computer could still work fine in that case. This is not a forced conclusion.
- 1, 4: 'Operating system fails' implying 'The computer works' runs directly opposite to the main statement, which says a failed operating system means the computer will not work. This pair contradicts the main statement.
- 4, 2: 'The computer works' implying 'Operating system does not fail' is exactly the contrapositive of the main statement. If the operating system had failed, the computer would not work, so a working computer guarantees the operating system did not fail.
Only the pairing of 'computer works' leading to 'operating system does not fail' is the logically forced flip side of the original conditional.
Therefore, the correct answer is 4, 2.
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Approach Solution -3
Let P stand for "operating system fails" and Q for "the computer will not work." The main statement, "The computer will not work if operating system fails," translates directly to P implies Q. The only statement guaranteed to follow from this is its contrapositive, not-Q implies not-P. Let's test each option:
- 2, 1: Statement 2 is not-P, "operating system does not fail," and statement 1 is P itself. Not-P implying P is a direct contradiction, never valid.
- 2, 3: Statement 2 is not-P and statement 3 is Q, "the computer does not work." The main statement only tells us what follows from P being true, it says nothing at all about what happens when P is false, so not-P implying Q is not something we can guarantee.
- 1, 4: Statement 1 is P and statement 4 is not-Q, "the computer works." P implies Q was given, so P implying not-Q directly contradicts the main statement.
- 4, 2: Statement 4 is not-Q, "the computer works," and statement 2 is not-P, "operating system does not fail." Not-Q implies not-P is exactly the contrapositive of P implies Q, and is therefore logically guaranteed.
Only the contrapositive pairing, not-Q implies not-P, is guaranteed to follow from the main conditional P implies Q.
Therefore, the correct answer is 4, 2.
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