Question

9.
Write a pair of integers for the following statements.
a) The sum is an integer smaller than both the integers.
b) The sum is greater than one of the integers.​

Answer 1

Answer:

both a and b

Step-by-step explanation:

hope it is helpful to you

Answer 2

Answer:

Complete step by step answer:

Let us assume two variables x and y . Now the sum of the two variables is given by x+y .

(i) The sum should be zero.

If the sum of the two variables is zero, then the value x+y should be equal to zero.

∴x+y=0⇒x=−y

From the above equation, we can say that if the sum of the two integers is zero, then the two integers are equal and having opposite signs. So, let us assume the integers as +5,−5 sum of these integers is +5−5=0 .

(ii) The sum should be a negative integer.

If the sum of the two variables is a negative integer i.e., the sum is less than zero.

∴x+y<0⇒x<−y

From the above equation, we can say that if the sum of the two integers is a negative number, then the one integer having a greater value should have a negative sign. So, let us assume the integers 2,−7. Now the sum of the above integers is 2+(−7)=2−7=−5 .

(iii) The sum should be smaller than both integers.

If the sum of the two variables is smaller than both the integers, then

x+y<y and x+y<x

⇒x<0 and y<0 .

From the above equation, we can say that if the sum of the two integers is smaller than both the integers, then the two integers are must be less than zero. So, let us assume the integers −2,−7 . Now the sum of the above integers is −2+(−7)=−2−7=−9 .

(iv) The sum should be greater than the two integers.

If the sum of the two variables is greater than both the integers, then

x+y>y and x+y>x

⇒x>0 and y>0 .

From the above equation, we can say that if the sum of the two integers is smaller than both the integers, then the two integers are must be greater than zero. So, let us assume the integers 2,7 . Now the sum of the above integers is 2+7=9.

(v) The sum should be less than one of the integers.

If the sum of the two variables is less than one of the integers, then

x+y<y or x+y<x

⇒x<0 or y<0 .

From the above equation, we can say that if the sum of the two integers is less than one of the integers, then one of the integers should be less than zero or a negative integer. So, let us assume the integers −2,7 . Now the sum of the above integers is −2+7=5.