The pumping lemma says that every regular language has a pumping length p$,$ such

that every string in the language can be pumped if it has length p or more. If p is a

pumping length for language A$,$ so is any length p$>=$ p$.$ The minimum pumping

length for A is the smallest p that is a pumping length for A$.$ For example, if

A $=01,$ the minimum pumping length is $2.$ The reason is that the string s $=0$ is

in A and has length $1$ yet s cannot be pumped; but any string in A of length $2$ or

more contains a $1$ and hence can be pumped by dividing it so that x $=0,$ y $=1,$

and z is the rest. For each of the following languages, give the minimum pumping

length and justify your answer.