what are these arrow operators in context free grammar?

Question

I'm studying context free grammar and I'm curious what the arrow with the star and the arrow without the star mean in parts f and g where:

• f is false.
• g is true.

Answer 1

"x ⇒ y" means that y can be derived from x in exactly one application of some production of the grammar. Putting an asterisk over the ⇒ means that y is derived from x via zero or more (but finitely many!) applications of some sequence of productions.

Answer 2

See http://en.wikipedia.org/wiki/Context-free_grammar#Repetitive_rule_application for an explanation.

That is to say, if u star-arrow v, there is some series of applications of rules that goes from u to v.