If 'a' is an odd number, which of the following is also odd? 3a + 1
о
a + 2
O +
2a + 2
a + 1​

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.

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.

37

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