Question

Write down a pair of integers, whose difference is -10.

Answer 1

Hint: The given problem is related to integers. Consider any integer and add -10 to it to get the other number. The selection of integers is random and hence there are infinite answers to this problem.

Complete step-by-step answer:

Before proceeding with the solution , let’s understand the concept of integers. Integers are a set of numbers, both positive and negative, along with 0, but which do not have any fractional part or decimals. We can say that integers are those rational numbers whose denominator is equal to 1. For example: -1, -2, 0, 1, 4, 5, etc. Integers have closure property which is satisfied by addition, subtraction and multiplication. The closure property for integers says that if two integers undergo a mathematical operation and the result is always an integer, then the closure property is said to be satisfied. In case of integers, addition, subtraction or multiplication of two integers always yields an integer, but division of integers may or may not yield an integer. Hence, integers are closed under addition, subtraction and multiplication, but not under division.

Now, coming to the question, we are asked to find a pair of integers, whose difference is -10. Let’s consider one of the integers to be x and the other to be y. So, according to the question,

we can say x – y = -10.

$\Rightarrow y-x=10$

Since any other constraint is not given, so we can assume x to be any integer, and then we will find the value of y corresponding to the assumed value of x.

So, let x = 1.

$\Rightarrow y-1=10$

$\Rightarrow y=10+1$

$\Rightarrow y=11$

Hence, (1,11) is our required pair.


Note: There is only one constraint for the pair of integers that their difference is -10. No other constraint is given. Because of this, we can assume x to be any integer. This results in an infinite number of pairs, hence giving infinite answers to this problem. Students should not get confused in this part. Any answer will be correct as long as it follows one condition, i.e. the difference between the integers is -10.