Consider the grammar with start symbol S and terminals a, b, with the rules: S aSb | SS | .

Choose all the correct statements about an arbitrary string in the language generated by this grammar.

The options refer to the following definitions:

A prefix of a string is any string for which there is a string such that =. Similarly, a suffix of a string is any string for which there is a string such that =. For instance, for a string =xyxyz, xyx is a prefix and xyz is a suffix (but not vice versa).

Choose one or more:

a. In any suffix of the string, number of a's number of b's

b. If the string is split into two equal parts, in each part, number of a's = number of b's

c. number of a's = number of b's

d. In any prefix of the string, number of a's number of b's

e. The string starts with an a

f. In any prefix of the string, number of a's = number of b's