Question

Determine whether the statement is sometimes, always, or never true. Give an example or counterexample. Negative - Positive = Negative.

A. Sometimes true
B. Always true
C. Never true
D. Unable to determine

Answer 1

The statement that a negative number minus a positive number equals a negative number is always true. This rule of arithmetic does not have any exceptions, hence no counterexample exists to disprove it.

Step-by-step explanation:

The statement "Negative - Positive = Negative" is always true. In mathematics, when you subtract a positive number from a negative number, the result is always a negative number. This is because subtracting a positive number makes the quantity smaller, and since we're starting with a negative number, it becomes more negative.

For example, if we take -5 and subtract +2, which we write as (-5) - (+2), the result is -7. This satisfies the given statement that a negative number minus a positive number equals a negative number.

A counterexample is used to demonstrate that a statement is not universally true. However, in this case, no counterexample exists because the stated relationship between negative and positive numbers is a consistent rule in arithmetic.