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4. For the following claims, state whether they are TRUE or FALSE. Statements claimed to be...

4. For the following claims, state whether they are TRUE or FALSE. Statements claimed to be TRUE must be accompanied by a proof, and statements claimed to be FALSE must be accompanied by a counterexample.

(a) Let A and B be events in the sample space S. Then P(A ∩ B) ≤ P(A)P(B).

(b) Let E be an event with 0 < P(E) < 1 and define PE(A) = P(A ∩ E) for every event A in the sample space S. Then PE satisfies the axioms of probability

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