Show that all binary strings generated by the following, Theory of Computation

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Show that all binary strings generated by the following

a) Show that all binary strings generated by the following grammar have values divisible by 3. Hint. Use induction on the number of nodes in a parse tree.

num -> 11 | 1001 | num 0 | num num

b) Does the grammar generate all binary strings with values divisible by 3?

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