Understanding the Closure Property

Which of the following illusirates the closure property of addition of real numbers?

A. The sum of any two numbers is close to the product of those numbers.

B. The sum of any two numbers is close to the difference of those numbers.

C. When you add 1 to a number you get the next closest number.

D. The sum of any two real numbers is also a real number.

Option D:

The sum of any two real numbers is also a real number.

Solution:

Closure property of addition of real numbers:

Sum of any two numbers is also a real number.

i. e., a + b = c

If a and b are real, then c is also a real number.

To find which illustrates the closure property of addition of real numbers:

Option A:

The sum of any two numbers is close to the product of those numbers.

It is not true because it is addition property not product.

Option B:

The sum of any two numbers is close to the difference of those numbers.

It is not true because it is addition property not difference.

Option C:

When you add 1 to a number you get the next closest number.

It is not true by the above definition.

Option D:

The sum of any two real numbers is also a real number.

This is the closure property of addition of real numbers.

It is true.

Hence the sum of any two real numbers is also a real number.

Option D is the correct answer.