Answer the following questions:

Question 1: Let A be any fixed finite set of 4 or more elements.

Prove that the number of subsets of elements in A is less than the number of permutation of elements of A

Question 2:  Let A = {0 ,1, 2}, and let language L be defined by L = {wa(w^R)bw|w belongs to A*}

Question 3:  what is |A^3| what is |A^n|  what is |A*|

Question 4: Thinking of L as a language, what is its alphabet? how many elements are there in L which have length 8

Answer these questions and show each and every step with example.