Question

You are supposed to find a pair of integers whose difference gives
A.A negative integer
B.Zero
C.An integer smaller than both the integers
D.An integer greater than only one of the integers
E.An integer greater than both the integers

Answer 1

Hint: We are supposed to find a pair of integers whose difference gives us required results so we pick and choose these values by careful observation and hit and trial method. The answer is not fixed meaning there can be multiple answers for one part.

Complete step-by-step answer:
Firstly we write what we want to obtain in each part of the question and then solve it separately.
In this part we want to obtain a negative integer by selecting a pair of integers. So one integer should be greater than the other and then we subtract the bigger one from the smaller one. So we select:
$
  2\;,4\; \in \mathbb{Z}\,{\text{such}}\,{\text{that}} \\
  2 - 4 = \; - 2 \in \mathbb{Z} \;
 $
This is our desired result.
In this part we select two same integers such that when we take the difference of them we get our desired outcome i.e.
$
  7 \in \mathbb{Z}\,{\text{such}}\,{\text{that}} \\
  7 - 7 = 0 \in \mathbb{Z} \;
 $
This is our desired result.
In this part we are supposed to select a pair so that after subtracting one from another we get a smaller values than the two so we select:
$
  9,5\; \in \mathbb{Z}\,{\text{such}}\,{\text{that}} \\
  9 - 5 = 4 \in \mathbb{Z}\; \\
  4 < 9,5 \;
 $
This is our desired result.
In this part we select a pair of integers so that the outcome is greater one of the selected ones, i.e.
$
  5\,,2 \in \mathbb{Z}\,{\text{such}}\,{\text{that}} \\
  5 - 2 = 3 \in \mathbb{Z} \\
  3 > 2\;\& \;3 < 5 \;
 $
This is the desired outcome.
In this part we select a pair of integers such that the outcome is greater than both the numbers i.e.
$
   - 3, - 5 \in \mathbb{Z}\,{\text{such}}\,{\text{that}} \\
   - 3 - ( - 5) = - 3 + 5 = 2 \in \mathbb{Z} \\
  2 > - 3, - 5 \;
 $
This is the desired result.

Note: The integers selected above in different parts of the question are not unique solutions but they are one of the solutions. We can choose other integers also which satisfy the given condition meaning that it totally depends upon the choice of an individual which pair of integers one wants to select.