Using induction on i $,$ prove that $(w^R{)}^i=(w^i{)}^R$ for any string w and all $i0.$

Hints: feel free to use the following Theorem in your proof

please answer all the question and exolain your process Let $u,$vin${}^{*},$ then $(uv{)}^R=v^R{u}^R.$

For the following exercises, give a regular expression that represents that described set.

The set of strings over $\{a,b,c\}$ in which all the a$\text{'}$s precede the b$\text{'}$s$,$ which in turn

precede the c$\text{'}$s$.$ It is possible that there are no a$\text{'}$s$,$ b$\text{'}$s$,$ or c$\text{'}$s$.$

The same as Exercise $2$ without the null string.

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