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

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

a. If P(a | b, c) = P(b | a, c), then P(a | c) = P(b | c)

b. If P(a | b, c) = P(a), then P(b | c) = P(b)

c. If P(a | b) = P(a), then P(a | b, c) = P(a | c)

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