Prove or give counterexamples to the following statements:
(a) If E is independent of F and E is independent of G, then E is independent of F ∪ G.
(b) If E is independent of F, and E is independent of G, and FG = ➢, then E is independent of F ∪G.
(c) If E is independent of F, and F is independent of G, and E is independent of FG, then G is independent of EF.
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