Let L be a subset of {a,b}*
Define a relation R   (R sub L) on S* as follows:
		   L

for All of x, y is a member of S*, 
(x,y) are members of R if for all of z, xz are members of L iff yz are members of L

A) Show that R is an equivalence relation

B) Suppose L={a^i b^i where i >= 0}
   What can you say about the index of R (number of classes)? is it finite or infinite? 
   Show some classes and elements in these classes to justify your answer?

c) Suppose L={a^i b^j where i,j  >= 0}
   What can you say about the index of R (number of classes)? is it finite or infinite? 
   Show some classes and elements in these classes to justify your answer?

D) Suppose L={a^i b^3i where i >= 0}
   What can you say about the index of R (number of classes)? is it finite or infinite? 
   Show some classes and elements in these classes to justify your answer?

Note: ^ means to the power, so a^i means a to the power of i.