The statement “When an integer is added to itself, the sum is greater than the integer” is
always true
never true
true only when the integer is positive
true for non-negative integers
Let the integer be \(n\).
When an integer is added to itself:
\[ n + n \]
This is the same as:
\[ 2n \]
Now compare \(2n\) with \(n\) in three simple cases.
Case 1: Positive integer
If \(n > 0\), then
\[ 2n > n \]
So the sum is greater than the integer.
Case 2: Zero
If \(n = 0\), then
\[ 2n = 0 = n \]
The sum is not greater; it is equal.
Case 3: Negative integer
If \(n < 0\), then
\[ 2n < n \]
The sum is smaller than the integer.
Conclusion: The statement is true only when the integer is positive.
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