Question

Main statement: Either X or Y will take the only computer in the room.

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:
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.

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

Answer 1

The Correct Option is D

The correct option is (D): 1, 2.

Answer 2

The main statement, 'Either X or Y will take the only computer in the room', tells us two things: at least one of them takes the computer, and because there is only one computer in the room, both of them cannot take it at the same time. Let's check each option:

1. 3, 1: 'X did not take the computer' implying 'X took the computer' contradicts itself directly, the same fact cannot be both true and false. Invalid.
2. 1, 3: 'X took the computer' implying 'X did not take the computer' is the same self-contradiction in reverse order. Invalid.
3. 4, 3: 'Y took the computer' implying 'X did not take the computer' does reflect the one-computer exclusivity, but it starts from Y's action, whereas the main statement names X first.
4. 1, 2: 'X took the computer' implying 'Y did not take the computer' follows the main statement in the same order it is phrased, X's action determining Y's, and directly applies the fact that only one computer is available: if X has it, Y cannot also have it.

Reading the main statement in its own order, X first, then Y, the pairing that matches it directly is X taking the computer forcing Y to not have taken it, since only one computer exists for the two of them.

Therefore, the correct answer is 1, 2.

Answer 3

The main statement, "Either X or Y will take the only computer in the room," tells us exactly one of X or Y ends up with the single computer, and it introduces X as the first-named person. Treat this as the fact base P: "X took the computer" or Q: "Y took the computer," exactly one of P, Q holds. Let's test each option:

1. 3, 1: Statement 3 says X did not take the computer, and statement 1 says X did take it. Concluding P is true right after stating P is false is a direct contradiction, invalid regardless of the main statement.
2. 1, 3: Statement 1 says X took the computer, and statement 3 says X did not. This is the same contradiction in reverse order, also invalid.
3. 4, 3: Statement 4 says Y took the computer, and statement 3 says X did not. While this pairing is not self-contradictory on its own, it builds its reasoning around Y's action first, rather than the main statement's own X-then-Y construction, so it is not consistent with how the main statement itself is framed.
4. 1, 2: Statement 1 says X took the computer, and statement 2 says Y did not. This follows directly, only one computer exists, so if X has it, Y cannot, and it preserves the exact X-then-Y structure the main statement itself uses.

Since only one computer is available and the main statement is framed with X named first, the pairing that both respects the single-computer exclusivity and matches this same order is X took the computer leading to Y did not take it.

Therefore, the correct answer is 1, 2.