1. If a and b are two odd positive integers such that a > b, then prov

1.	1. If a and b are two odd positive integers such that a > b, then prove that one of the two numbers a+b/2and a-b/2 is odd and the other is even.
Answer» Answer: Now we know that, odd number + *odd* number = *even* *number* *even* number + even number = *even number similarly, odd* *number* + *even number = odd* *number* *even* number + *odd* *number* = *odd* *number* Keeping these in mind, a + b is an even number and similarly a - b is also an even number. so, $\frac{(a + b)}{2} \: + \: \frac{(a - b)}{2} \: = \: \frac{2a}{2} = a$ which is an odd number. hence from above statements we can say that among $\frac{a + b}{2} \: and \: \frac{a - b}{2}$ ONE of them should be an odd number and the other should be an even number otherwise the SUM will not be an odd number. hence one of the two numbers a+b/2and a-b/2 is odd and the other is even. hence proved. PLEASE MARK ME AS THE BRAINLIEST. I HAVE DONE MY BEST TO MAKE IT EASILY UNDERSTANDABLE. PLEASE IGNORE IF YOU FIND ANY GRAMMATICAL MISTAKES.

1. If a and b are two odd positive integers such that a > b, then prove that one of the two numbers a+b/2and a-b/2 is odd and the other is even.

Answer»

Answer:

Now we know that,

odd number + odd number = even number

even number + even number = even number

similarly,

odd number + even number = odd number

even number + odd number = odd number

Keeping these in mind,

a + b is an even number and similarly

a - b is also an even number.

so,

$\frac{(a + b)}{2} \: + \: \frac{(a - b)}{2} \: = \: \frac{2a}{2} = a$

which is an odd number.

hence from above statements we can say that among

$\frac{a + b}{2} \: and \: \frac{a - b}{2}$

ONE of them should be an odd number and the other should be an even number otherwise the SUM will not be an odd number.

hence one of the two numbers a+b/2and a-b/2 is odd and the other is even.

hence proved.

PLEASE MARK ME AS THE BRAINLIEST.

I HAVE DONE MY BEST TO MAKE IT EASILY UNDERSTANDABLE.

PLEASE IGNORE IF YOU FIND ANY GRAMMATICAL MISTAKES.