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Constructing Direct Proofs so i am working with my hw and i get stuck. problem: if...

Constructing Direct Proofs

so i am working with my hw and i get stuck.

problem:

if a is an integer, b is an odd integer, and c is an even integer, then a( b-c ) is an odd integer.

I need a known show table and then a complete proof for this problem.

for now i only set up hypothesis and definition of odd and even, and set it = to a(b-c) and not sure whats next~

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