Question: For the statements listed below, show that it is true, or if it is false, give a counterexample. If P(a|b, c) = P(a), then P(b|c)

For the statements listed below, show that it is true, or if it is false, give a counterexample.

  1. If P(a|b, c) = P(a), then P(b|c) = P(b).
  2. If P(a|b) = P(a), then P(a|b, c) = P(a|c).
  3. P(a|b, c) = P(b|a, c), then P(a|c) = P(b|c).
  4. P(a|b a) = 1.

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