Question

Let a be any integer, except zero. Which statement is never true?

a. lal = -a
b. la|> 0
c. a> -a
d. -la|= lal

Answer 1

The statement |a| = -a is never true for any non-zero integer a, as the absolute value of a number is always non-negative.

Step-by-step explanation:

The question Let a be any integer, except zero. Which statement is never true? involves understanding the properties of absolute value and the relationship between a number and its negative. We'll analyze each provided option:

• Option a: |a| = -a: This statement is never true since the absolute value of a number is always non-negative, so |a| cannot be equal to a negative unless a is 0, which is excluded by the question.
• Option b: |a| > 0: This statement is always true for all non-zero integers a.
• Option c: a > -a: This statement is always true for all positive integers and false for negative integers. However, it is not never true.
• Option d: -|a| = |a|: This statement is never true for non-zero integers since it would imply that a is both non-negative and non-positive, which is contradictory.

Therefore, the statement that is never true for any non-zero integer a is: |a| = -a.