Which of the statement(s) is/are incorrect? (1) If \( f+g \) is con...

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Which of the statement(s) is/are incorrect?
(1) If \( f+g \) is continuous at \( x=a \), then \( f \) and \( g \) are continuous
\( \mathrm{P} \) at \( x=a \).

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(2) If \( \lim _{x \rightarrow a}(f g) \) exists, then both \( \lim _{x \rightarrow a} f \) and \( \lim _{x \rightarrow a} g \) exist.
(3) Discontinuity at \( x=a \Rightarrow \) non-existence of limit.
(4) All functions defined on a closed interval attain a maximum or a minimum value in that interval.
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