For each of the following statements, either prove it is true or give a
counterexample.

1. If $P(a b, c) = P(b a, c)$, then $P(a c) = P(b c)$

2. If $P(a b, c) = P(a)$, then $P(b c) = P(b)$

3. If $P(a b) = P(a)$, then $P(a b, c) = P(a c)$

1. If $P(a b, c) = P(b a, c)$, then $P(a c) = P(b c)$

2. If $P(a b, c) = P(a)$, then $P(b c) = P(b)$

3. If $P(a b) = P(a)$, then $P(a b, c) = P(a c)$

1. If $P(a b, c) = P(b a, c)$, then
$P(a c) = P(b c)$

2. If $P(a b, c) = P(a)$, then $P(b c) = P(b)$

3. If $P(a b) = P(a)$, then
$P(a b, c) = P(a c)$