State whether the following statement is true or false:

The absolute value of an integer is greater than the integer.

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True

False

answer is B.

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Detailed Solution

The given statement is false.
Concept- Here, we use the definition of an integer's absolute value to compare the magnitudes of the two numbers. The modulus of an integer is its absolute value.
We are aware that the set of integers can be expressed as

and that it contains all the negative numbers, zero, and all the positive numbers.
Integers are therefore stretched on both sides of a real line.
We now understand that the absolute value of an integer is the integer's numerical value without taking the sign into account. A modulus sign (|x|) indicates an integer's absolute value.
If

is positive, the value of

.
If

is negative, the value of

.
An integer's absolute value is never negative since when we apply a modulus to it, the negative sign is also erased.
In other words, the entire real line (with the exception of negative numbers) is where the absolute values of integers are represented.
If we take the integer

, its absolute value will be

, which is a positive number. Therefore, we can state that an integer's absolute value exceeds the integer.
If we take the integer

, its absolute value will be

, which is a positive number. Therefore, we can assert that an integer's absolute value is equal to the integer.
Both of the aforementioned statements lead us to the conclusion that an integer's absolute value is higher than or equal to its value.
Therefore, the statement in the question is incorrect.
Hence, the given statement is false.

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