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: Either X or Y will take the only computer in the room.
Statements: 1. X took the computer.
2. Y did not take the computer.
3. X did not take the computer.
4. Y took the computer.
The ordered pair of statements is:

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In "either/or" logic questions, make sure each statement logically complements the main statement without contradicting the options. In "either A or B", one must be true, but not both.
Updated On: Jul 15, 2026
  • 3, 1
  • 1, 3
  • 4, 3
  • 1, 2
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The Correct Option is D

Approach Solution - 1

Since there is only one computer, X and Y cannot both take it, so knowing one of them took it tells us the other did not.

  1. 3, 1: "X did not take it" cannot force "X took it", a direct contradiction.
  2. 1, 3: "X took it" cannot force "X did not take it" either, the reverse contradiction.
  3. 4, 3: reverses the order the main statement sets up between X and Y, so it is not the pair being asked for here.
  4. 1, 2: X taking the one computer directly rules out Y taking it, matching the main statement exactly in the same order it names X and Y.

So the correct answer is 1, 2.

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Approach Solution -2

Let \( X \) mean "X took the computer" and \( Y \) mean "Y took the computer." Because there's only one computer and one of the two must take it, exactly one of \( X \), \( Y \) is true at a time, giving \( X \leftrightarrow \neg Y \).

  1. 3, 1 (\( \neg X \), so \( X \)): asks \( \neg X \) to imply \( X \) directly, contradicting itself without even using the biconditional.
  2. 1, 3 (\( X \), so \( \neg X \)): the same contradiction in reverse.
  3. 4, 3 (\( Y \), so \( \neg X \)): follows from \( X \leftrightarrow \neg Y \) too, but states the relationship starting from \( Y \) rather than from \( X \), the term the main statement names first.
  4. 1, 2 (\( X \), so \( \neg Y \)): follows directly from \( X \leftrightarrow \neg Y \), starting from \( X \) exactly as the main statement does.

Therefore, the correct answer is 1, 2.

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Top Questions on Statements

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