Answer Happy

Give a BNF grammar for each of the languages below. For example,
a correct answer for “the set of all strings consisting of zero or
more concatenated copies of the string “ab” would be this
grammar:
<S> ::= ab <S> | <empty>
(2 points) The set of all strings consisting of one or more
instances of the letter a.
(3 points) Show that your grammar can derive the following
sentences:
a
aa
aaa
(2 points) The set of all strings consisting of one or more
instances of the letter a with a semicolon after each one.
(3 points) Show that your grammar can derive the following
sentences:
a;
a; a;
a; a; a;
(2 points) The set of all strings consisting of an uppercase
letter followed by zero or more additional characters, each of
which is either an uppercase letter or one of the digits 0 through
9.
(3 points) Show that your grammar can derive the following
sentences:
A
AA
A1
AA1
A1A
(2 points) The set of all strings consisting of an open bracket
(the symbol [ ) followed by a list of one or more digits separated
by commas, followed by a closing bracket (the symbol ] ). Note that
the digits are 0 through 9.
(3 points) Show that your grammar can derive the following
sentences:
[0]
[0,1]
[0,1,2]