Construct context-free grammars that generate the given set of strings.

Construct context-free grammars that generate the given set of strings. If the grammar has more than one variable, we will ask to create a sentence describing what sets of strings expect each variable in the grammar to generate. For example, if the grammar was:

I could say "C generates binary strings of length one, E generates (non-empty) even length binary strings, and O generates odd length binary strings." It is also fine to use a regular expression, rather than English, to describe the strings generated by a variable (assuming such a regular expression exists).

(a) Binary strings matching the regular expression "(1 ∪ 01 ∪ 001)∗ (0 ∪ ε)".

Hint: use the procedure described in lecture to convert the RE to a CFG