According to the trichotomy law, for any real numbers X and Y, which statement is always true?

According to the trichotomy law, for any real numbers X and Y, which statement is always true?

• A. X > Y
• B. One of X > Y, X = Y, or Y > X
• C. X = Y
• D. Y < X

Answer: (B)

In real numbers, for any two numbers X and Y exactly one of these relations holds: X > Y, X = Y, or X < Y. This is the trichotomy property. Therefore, the statement that one of X > Y, X = Y, or Y > X must be true for any pair is always true. Note that Y > X is the same as X < Y, so this set of possibilities covers every case. X > Y alone isn’t always true because X could be equal to Y or less than Y. X = Y alone isn’t always true because the numbers could be different. Y < X isn’t always true because X could be greater or equal to Y.

In real numbers, for any two numbers X and Y exactly one of these relations holds: X > Y, X = Y, or X < Y. This is the trichotomy property.

Therefore, the statement that one of X > Y, X = Y, or Y > X must be true for any pair is always true. Note that Y > X is the same as X < Y, so this set of possibilities covers every case.

X > Y alone isn’t always true because X could be equal to Y or less than Y. X = Y alone isn’t always true because the numbers could be different. Y < X isn’t always true because X could be greater or equal to Y.