Answer: B) a+2
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Step-by-step explanation:
Adding an even number to an odd number always results in an odd number
even + odd = odd
odd + even = odd
So if 'a' is odd, adding 2 onto it (even number), leads to an odd result of a+2.
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Extra Information (optional section)
If you are curious why the two equations shown above are true, then here's a proof.
Let 'a' be an odd number. This means a = 2k+1 for some integer k. We add 1 to any multiple of 2 and it goes from even (2k) to odd (2k+1).
If we made b an even number, then b = 2m for some integer m.
Adding 'a' and b gives us...
c = a + b
c = ( a ) + ( b )
c = ( 2k+1 ) + ( 2m )
c = (2k+2m) + 1
c = 2(k+m) + 1
c = 2n + 1 .... where n = k+m
The result a+b is an odd number since it is in the form 2*(integer)+1
It verifies the claim that odd+even = odd.
So this shows that a+2 is also odd, since we let b = 2.