I wonder which statements below are true/false, and also the reasons if they are false.

1. There exists a general algorithm to remove ambiguity
from a context-free grammar.
2. There is an algorithm that can tell whether a CFG is
ambiguous or not.
3. For every ambiguous CFG, there exists an equivalent yet
unambiguous CFG.
4. The language {ww^R} can be accepted by some DPDA.
5. Context-free languages are closed under union, concatenation,
and closure.

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