Q. 14.0( 268 Votes )
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.
Answer :
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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