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Prove or disprove each of the following statements: (a) There exist regular languages that are not context-free. (b) Every NFA has an equivalent DFA.

Prove or disprove each of the following statements: (a) There exist regular languages that are not context-free. (b) Every NFA has an equivalent DFA. (c) The intersection of two context-free languages is also context-free. (d) The union of two regular languages is not always regular. (e) There exist context-free languages that are not regular. Note that simply writing True or False is not enough. Provide a sound proof of your claim.

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