Answer

Verified

379.5k+ views

**Hint:**To solve this question, we need to know the basic theory related to the number system. as we know a number is an arithmetic value that is used to express the quantity of an object and helps in making calculations. Here, we will have a look at the definition, examples, and properties of even and odd numbers in detail.

**Complete step-by-step solution:**As we know, an even integer is defined as an integer which is the product of two and an integer while an odd integer is defined as an integer which is not even.

Let x and y be two odd numbers.

Then $x=2m+1$ for some natural number m and $y=2n+1$ for some natural number n.

Let’s take out their sum.

Thus $x+y=2m+1+2n+1=2(m+n+1)$

Here, with the addition 2 in there.

Therefore, $x+y$ is divisible by 2 and is even.

Here, we showed that if we add two odd numbers, the sum is always an even number.

To better convince ourselves that the given statement has some truth to it. We can test the statement with a few examples.

Now,

Let 1 and 3 be two odd numbers.

As we know, the sum of these two (1 and 3) is 4.

Which is divisible by 2 and as we know any number that can be exactly divided by 2 is called an even number.

Therefore, we conclude that the given statement is true.

**Hence, We prove that the sum of two odd numbers is even.**

**Note:**The sets of even and odd numbers can be expressed as follows,

Even = ${2k : k \in Z}$

Odd = ${2k + 1 : k \in Z}$

A formal definition of an even number is an integer of the form $n = 2k$, where k is an integer. An odd number is defined as an integer of the form $n = 2k + 1$. This classification applies only to integers. Non-integer numbers like $\dfrac{1}{2}$, 4.201, or infinity are neither even nor odd.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Describe the poetic devices used in the poem Aunt Jennifers class 12 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

And such too is the grandeur of the dooms We have imagined class 12 english CBSE

Where is the endless fountain of immortal drink pouring class 10 english CBSE

What I want should not be confused with total inactivity class 12 english CBSE

Why was the Moral Rearmament Army welcomed at the class 12 english CBSE

Difference Between Plant Cell and Animal Cell