Give a regular expression for each of the following sets:

$$ The set of strings over $\{$a$,$ b$\}$ that contain the substring aa and the substring bb$.$

$$ The set of strings over $\{$a$,$ b$,$ c$\}$ with length greater than three.

$$ The set of strings over $\{$a$,$ b$\}$ that do not end with ba$.$

$$ The set of all strings over $\{0,1\}$ with an equal number of $0$s and $1$s$,$ such that each prefix has at

most one more $0$s than $1$s and at most one more $1$s than $0$s$.$

$$ Set L $=\{$w $|$ w $2($a $+$ b$)$ and no two consecutive characters are the same$\}.$ Note that by the

definition of the set, the following strings are all in L$1$: $,$ a$,$ and b$,$ in addition to many others

such as ab$,$ bab, abab, ababa, etc.

$$ The set over $\{0,1\}$ that contains all the strings of $1$s whose length is a multiple of $2$ or $3.$

$$ The set of strings over $\{0,1\}$ where the number of $01$s is not the same as the number of $10$s$.$ For

example, $010$ is not in the set as we have one $01$ and one $10$;