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.