The pumping lemma says that every regular language has a pumping length p, such the 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 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. Please give the minimum pumping length and explain why.

a) 1001

b) 1*01*

c)11*00*1

d)(101)*0

e)101 U 1*0