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How would you prove that the sum of an even number and an odd number is always an odd number?
TrogdortheBurninator
Suppose x is an even number and y is an odd number.
Then x = 2*n for some integer n
and y = 2*m + 1 for some integer m
Therefore x + y = 2*n + 2*m + 1 = 2*(n + m) +1
Now, since n and m are integers, (n + m) is also an integer [by the closure of integers under addition].
Thus, x + y = 2*p + 1 where p = n + m is an integer.
ie x + y is an odd integer.
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The difference of two even number is always an even number?
Yes, the difference between two even numbers is always an even number.
6 is an even number prove it?
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