In every problem but the last one, you must use the successor function (s) and/or the predecessor function (pr) when working with natural numbers in order to have a chance at receiving full credit.

1. Assume that has 4 symbols: c, d, =, and ; .

a. Write a recursive definition for the language

{cc=dd; , cc=dd;cc=dd;cc=dd ; cc = dd;cc=dd;cc=dd;cc=dd;cc=dd; , ...}. (10 points)

b. Write a recursive definition for the language {d=c; , d=c;c=d; , d=c;c=d;d=c; , ...}. (10 points)