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