$($Graded for completeness$)$ Regular expressions $(10$ points$)$:

$($a$)$ Give three regular expressions that all describe the set of all strings over $\{a,b\}$ that have

even length. Ungraded bonus challenge: Make the expressions as different as possible!

$($b$)$ A friend tells you that each regular expression that has a Kleene star $(*)$ describes an infinite

language. Are they right? Either help them justify their claim or give a counterexample to

disprove it and then fix the formula.