For each of the following statements, either prove it is true or give a counterexample.
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If $P(a b, c) = P(b a, c)$, then $P(a c) = P(b c)$
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If $P(a b, c) = P(a)$, then $P(b c) = P(b)$
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If $P(a b) = P(a)$, then $P(a b, c) = P(a c)$
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