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

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

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

Answer: (C)

The main idea here is that real numbers are totally ordered. For any two numbers X and Y, exactly one of these must hold: X is greater than Y, X equals Y, or X is less than Y (which is the same as Y being greater than X). This is why the statement that lists these three possibilities is always true. It covers all outcomes and there’s no case where none or more than one of these can be true. For example, if X is 3 and Y is 5, the truth is Y > X; if X and Y are both 4, X = Y; if X is -2 and Y is 0, again Y > X.

The main idea here is that real numbers are totally ordered. For any two numbers X and Y, exactly one of these must hold: X is greater than Y, X equals Y, or X is less than Y (which is the same as Y being greater than X). This is why the statement that lists these three possibilities is always true. It covers all outcomes and there’s no case where none or more than one of these can be true. For example, if X is 3 and Y is 5, the truth is Y > X; if X and Y are both 4, X = Y; if X is -2 and Y is 0, again Y > X.