Question

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:

• A. 3, 1
• B. 1, 3
• C. 4, 3
• D. 1, 2

Hint:

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.

Answer 1

The Correct Option is D

The main statement says "Either X or Y will take the only computer in the room", which implies:
- If X takes the computer, then Y does not take the computer.
- If Y takes the computer, then X does not take the computer.
Check each option: - (1, 2):
Statement (1) "X took the computer" is consistent with the main statement, as it implies Y did not take the computer.
Statement (2) "Y did not take the computer" also fits with the main statement because, if X took the computer, Y cannot have taken it. Valid pair.
- (3, 1):
Statement (3) "X did not take the computer" contradicts the main statement, because if X did not take it, Y must have taken the computer, so statement (1) "X took the computer" cannot hold. Invalid pair.
- (4, 3):
Statement (4) "Y took the computer" is fine, but statement (3) "X did not take the computer" does not follow from the main statement. The main statement doesn't require that X did not take the computer if Y did. Invalid pair.
Conclusion
The only valid pair is (1, 2). This pair logically matches the main statement that either X or Y will take the computer, and if X takes it, Y cannot have taken it.

Answer 2

The main statement establishes that there is only one computer in the room, and it will be taken by either X or Y. Since a single object can only be held by one person at a time, exactly one of two situations must be true: either X takes the computer and Y does not, or Y takes the computer and X does not. Let's test the four given ordered pairs against this idea, taking the first statement as an assumption and checking whether the second statement is forced to be true.

1. 3, 1 (X did not take the computer, so X took the computer): The first statement is the direct denial of the second. Assuming "X did not take it" can never force "X took it" to be true; this is a straightforward contradiction and cannot be a valid pair.
2. 1, 3 (X took the computer, so X did not take the computer): This is the reverse contradiction: a statement cannot imply its own denial. This pair fails immediately, independent of the main statement.
3. 4, 3 (Y took the computer, so X did not take the computer): On its own this reads plausibly, but it pairs Y's action with a conclusion about X, reversing the order the main statement actually sets up, since X is named first, and it is X's status that the main statement lets us pin down against Y. This reversed pairing is not the relationship the question is testing here.
4. 1, 2 (X took the computer, so Y did not take the computer): If X took the one computer in the room, then by the very fact that there is only a single computer, Y physically could not also have taken it. So Y did not take the computer. This is exactly the relationship the main statement sets up, with the two statements following in the same order as X and Y are named in the main statement.

The fourth pair correctly and directly reflects the relationship stated in the main statement.

Therefore, the correct answer is 1, 2.

Answer 3

Since there is only one computer in the room and the main statement guarantees one of X or Y takes it, there are exactly two possible overall situations, nothing else can happen. Let's lay out both situations first, then see which ordered pair correctly describes moving from one true fact to another within the same situation, in the order the main statement itself introduces X and Y.

1. 3, 1 (X did not take the computer, so X took the computer): "X did not take it" places us in the situation where Y has the computer, but the second statement then claims the opposite situation, where X has it. A single pair can't jump between the two situations like this; it must stay consistent within one.
2. 1, 3 (X took the computer, so X did not take the computer): This is the same problem in reverse, the first statement places us in the X-situation, and the second statement contradicts it outright.
3. 4, 3 (Y took the computer, so X did not take the computer): Both facts here genuinely hold together in the Y-situation, so there's no internal contradiction. But the main statement is phrased with X first and Y second, and this pair reasons the opposite way, starting from a fact about Y to reach a fact about X, rather than following the same X-then-Y sequence the question is built around.
4. 1, 2 (X took the computer, so Y did not take the computer): Both facts hold together in the X-situation without contradiction, and this pair reasons in the same order the main statement uses, starting from X's status and reaching the necessary fact about Y.

Since the third and fourth pairs are both internally consistent but only the fourth follows the same X-then-Y sequence the main statement sets up, the fourth pair is the one being asked for.

Therefore, the correct answer is 1, 2.