$1.$ While passwords generally have few restrictions, they are normally not totally

free. Suppose that in a certain system, passwords can be of arbitrary length

but must contain at least one letter, a$$z$,$ and one number $09.$ Construct a

grammar that generates the set of such legal passwords.

$2.$ Suppose that in some programming language, numbers are restricted as

follows:

$($a$)$ A number may be signed or unsigned.

$($b$)$ The value field consists of two nonempty parts, separated by a decimal

point.

$($c$)$ There is an optional exponent field. If present, this field must contain

the letter e$,$ followed by a signed two$-$digit integer.

Design a grammar set of such numbers.

$3.$ Give a grammar for the set of integer numbers in C$.$

$4.$ Design an accepter for integers in C$.$

$5.$ Give a grammar that generates all real constants in C$.$