Question

If n is a real , then n is greater than or equal to the absolute value of n. Which of the following would be a counterexample?

A) n= 0
B) n=10
C) n=-2
D) n=5

Answer 1

The correct answer is C) n=-2, as it is the only option where n is not greater than or equal to the absolute value of n, thereby serving as a counterexample to the given statement.

Step-by-step explanation:

When considering the statement, 'If n is a real number, then n is greater than or equal to the absolute value of n', we can analyze each option to find a possible counterexample.

• A) n= 0: The absolute value of 0 is 0, so n is equal to its absolute value. This does not serve as a counterexample.
• B) n=10: The absolute value of 10 is 10, so n is equal to its absolute value. This does not serve as a counterexample.
• C) n=-2: The absolute value of -2 is 2, and -2 is not greater than or equal to 2. This is a counterexample to the given statement.
• D) n=5: The absolute value of 5 is 5, so n is equal to its absolute value. This does not serve as a counterexample.

The correct answer is C) n=-2, as it disproves the statement and serves as a counterexample.