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The Answer:We know the following properties of the parities concerning the numbers:

odd + odd = even

even + odd = odd (commutativity yields the vice verca possible too)

even + even = even

Thus, we know that the group of numbers have at least 1 odd. However, since 2 odds make an even, any amount of even amount of odds make an even. Therefore, there must be an odd number of odds (i.e., {1, 3, 5}, the only ones that exist in that set).

QED.

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