Exercises Let E = {a,b}. Let A = {w• w*lw e X*}. Prove that A sm A. O A is the language of palindromes over E of even length. 1. Construct a mapping reduction from A to A. Write Grafstates code to...

Extracted text: Exercises Let E = {a,b}. Let A = {w• w*lw e X*}. Prove that A sm A. O A is the language of palindromes over E of even length. 1. Construct a mapping reduction from A to A. Write Grafstates code to implement your mapping reduction function. 2. Prove that your mapping reduction function has the mapping reduction property.