SOLUTION: if x and y are odd numbers, then x+y is even If x and y are both odd, then x+1 and y-1 are even. But then x+y=(x+1)+(y-1) is the sum of two even numbers, and, therefore, even.

Algebra ->  Proofs -> SOLUTION: if x and y are odd numbers, then x+y is even If x and y are both odd, then x+1 and y-1 are even. But then x+y=(x+1)+(y-1) is the sum of two even numbers, and, therefore, even.       Log On


   

Question 1021264: if x and y are odd numbers, then x+y is even
If x and y are both odd, then x+1 and y-1 are even. But then x+y=(x+1)+(y-1) is the sum of two even numbers, and, therefore, even.
Is this a valid proof? If so, what type of proof is it because I am confused.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
if x and y are odd numbers, then x+y is even:: True
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If x and y are both odd, then x+1 and y-1 are even.:: True
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But then x+y=(x+1)+(y-1) is the sum of two even numbers
and, therefore, even::
Is this a valid proof? If so, what type of proof is it because I am confused.
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It shows that "if x and y are odd, the sum of x+1 and y-1 is even.
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Cheers,
Stan H.
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