Question:medium

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.
Statements: 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:

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When analyzing conditional statements, remember that the contrapositive is also valid. If "If A, then B" holds, then "If not B, then not A" also holds.
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 rule given is simple: if the operating system fails, the computer definitely will not work. We check which pair is a forced consequence of that rule.

  1. 2, 1: not failing cannot force failing, that is a straight contradiction.
  2. 2, 3: the rule says nothing about what happens when the operating system does not fail, so this jump is not actually guaranteed.
  3. 1, 4: this says failure leads to the computer working, the opposite of the rule.
  4. 4, 2: if the computer is working, the operating system cannot have failed, since a failed system would have stopped it from working. This is the one pair that has to be true.

So the correct answer is 4, 2.

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Approach Solution -2

The main statement forbids exactly one combination of the two ideas: the operating system failing while the computer still works. The combinations left possible are OS fails with the computer not working, OS does not fail with the computer working, and OS does not fail with the computer not working. Let's check each pair against this list.

  1. 2, 1 (not failed, failed): these two statements describe opposite states of the same thing at once, so this pair fails on its own, without even checking the allowed list.
  2. 2, 3 (not failed, not working): "not failed" appears in two of the allowed combinations, computer working and computer not working, so knowing only that the OS didn't fail doesn't fix whether the computer works. This pair assumes a certainty the statement doesn't actually give.
  3. 1, 4 (failed, working): this is precisely the one forbidden combination, so it goes directly against the main statement.
  4. 4, 2 (working, not failed): "computer working" appears only in the allowed combination paired with "OS does not fail," never with "OS fails," so a working computer guarantees the OS did not fail.

Since 4, 2 is the only pair that matches an allowed combination without any ambiguity, the correct answer is 4, 2.

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