What I ended up doing, in response to Adam's message, is figuring that:
$ x_1[n] = -x_1[-n] $ and $ x_2[n] = x_2[-n] $ and then defined $ (x_1[n])(x_2[n]) $ as y[n]
Multiplying the redefined $ x_1[n] $ and $ x_2[n] $ I got $ -(x_1[-n](x_2[-n])) $ which resembles very closely -y[-n]. From there I declared the function odd.
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