The term 'either' in logical statements excludes the possibility of both being true.

The term 'either' in logical statements excludes the possibility of both being true.

• A. Sometimes true
• B. False
• C. True
• D. Not applicable

Answer: (B)

The key idea is the difference between exclusive and inclusive use of “or” in logic. In formal logic, A or B (the OR connective) is true if at least one of A or B is true, and it can be true even if both are true. If you want to say that exactly one is true and not both, you would use “either A or B, but not both” or something like XOR. So the statement that “either” excludes the possibility of both being true is not universally true. There can be situations where both A and B are true, and the expression “either A or B” would still be true in that case. That’s why the statement is false. For example, if A is “it is raining” and B is “it is snowing,” both can occur at the same time, and the claim would fail.

The key idea is the difference between exclusive and inclusive use of “or” in logic. In formal logic, A or B (the OR connective) is true if at least one of A or B is true, and it can be true even if both are true. If you want to say that exactly one is true and not both, you would use “either A or B, but not both” or something like XOR.

So the statement that “either” excludes the possibility of both being true is not universally true. There can be situations where both A and B are true, and the expression “either A or B” would still be true in that case. That’s why the statement is false. For example, if A is “it is raining” and B is “it is snowing,” both can occur at the same time, and the claim would fail.