# If a and b are two odd positive integers such that a > b, then prove that one of the two numbers and is odd and the other is even.

Given: a and b are two odd positive integers such that a>b.
To prove: out of the numbers  one is odd and other is even.
Proof:  a and b both are odd positive integers,
Since,

which is an odd number as "a" is given to be a odd number.
Hence one of the number out of must be even and other must be odd because adding two even numbers gives an even number and adding two odd numbers gives an even number.
Here, will give an odd number and will give an even number.

EXAMPLE:

Take a = 7 and b = 3 such that a>b

Now,  which is odd

And  which is even
Conclusion: Out of out of the numbers  ,
is an odd number and is an even number.

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