Consider the grammar with start symbol S and terminals a, b, with the rules: S → aSb | SS | ε . 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 σ is any string α for which there is a string β such that σ=αβ. Similarly, a suffix of a string σ is any string β for which there is a string α such that σ=αβ. For instance, for a string σ=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