Question

❤❤HELLO...!!!❤❤



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

✔NEED A PROPER PROOF
✔NUMBERS AREN'T TO BE TAKEN IN PLACE OF a AND b
✔NO SPAM SHOULD BE DONE
✔DO NOT COPY FROM GOOGLE



ALL THE BEST...!!!​

Answer 1

if a and b even

a+ b and a-b both even

that means both have 2 as factor

so divisible by 2

now if a= 2k( k odd) ,b = 2s ( s even)

a+ b= 2 ( k+ s)

k+ s = odd + even = odd ,k-s would be odd also

so both a+b)/2, a- b)/2 becomes odd

if a= 2k , b= 2s both k,s even

then a+b)/2, a-b)/2 both even

for both odd , still even odd + odd = even

if a and b odd

a+b, a - b even

2n +1, 2k +1 take a and b

a+b)/2 = n+ k +1

if n and k odd then odd + odd +1 = odd

obviously a-b/2 odd

still

a-b /2 = n - k , Soodd

if n,k both even, even+ even +1 = odd

But now a-b)/2 = even - even = even

So Now a+b)/2 odd, a-b)/2 even

for n,k odd,even odd+ even+1 = even

but a-b)/2 = odd - even = odd

So now also a+b)/2 even a-b)/2 odd

Answer 2

Step-by-step explanation:

your answer is in the above attachment