Question

sum of an odd number and an even number is always odd.true or false.give reasons​

Answer 1

It is always TRUE that sum of an odd integer and an even integer is always an odd integer.

Some examples are given below:

1. 2 + 3 = 5

2. 3 + 6 = 9

3. 7 + 4 = 11

4. 23 + 48 = 71

5. 75 + 64 = 139

Now this concept is going to be proven algebraically.

Odd integers and even integers are differ from each other mostly of the fact that, they leave remainder 1 and 0 respectively on division by 2.

As an odd integer leaves remainder 1 on division by 2, it is in the form '2q + 1' where q is some integer.

As an even integer leaves remainder 0 on division by 2, it is in the form '2q' where q is some integer.

Thus the sum of an odd integer and an even integer also...

2q + 1 + 2q

=> 4q + 1

=> 2(2q) + 1

=> 2m + 1 [m = 2q]

... leaves remainder 1 on division by 2. So it's an odd integer.

Hence Proved!

Answer 2

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Yes, it is True.

Examples:-

1. 1 + 2 = 3
2. 2 + 3 = 5
3. 3 + 4 = 7


4. 7 + 2 = 9