Question:medium

Main statement: The computer will not work if operating system fails.
  1. Operating system fails.
  2. Operating system does not fail.
  3. The computer does not work.
  4. 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.

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 main statement says an operating system failure guarantees the computer will not work, in short, OS fails implies computer does not work.

The only safe reversal is the contrapositive: if the computer is working, the operating system cannot have failed, giving 'computer works' leading to 'OS does not fail', exactly statements 4 and 2 in that order.

The remaining pairs either contradict themselves directly, reverse the original conditional's direction, or claim something the main statement never actually guarantees, namely what happens when the system does not fail.

Therefore, the correct answer is 4, 2.

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Approach Solution -2

"The computer will not work if operating system fails" tells us that an operating system failure is enough on its own to guarantee the computer stops working, it is a sufficient condition for the computer failing.

  1. 2, 1: Concluding that the operating system fails from the fact that it does not fail is a plain contradiction in the same sentence.
  2. 2, 3: Knowing the operating system did not fail tells us nothing definite about the computer, it could still fail for some other unrelated reason, so we cannot guarantee the computer does not work from this alone.
  3. 1, 4: If the operating system fails, we are told directly the computer will not work, so concluding the computer works instead contradicts the main statement outright.
  4. 4, 2: If the computer is working right now, then the one thing guaranteed to break it, an operating system failure, cannot have happened, so the operating system must not have failed.

Since an operating system failure is sufficient to stop the computer working, a working computer rules out that failure entirely, exactly the pairing of statements 4 and 2.

Therefore, the correct answer is 4, 2.

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