(Solution) - In problems decide whether the given statement is true or -(2025 Original AI-Free Solution)

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In problems decide whether the given statement is true or false. Then justify your answer.
(a) If f is continuous and f(x) ? 0 for all x in [a, b] then

(b) If

Then f(x) ? 0 for all x in 'a, b]
(c) If

Then f(x) = 0 for all x in [a, b]