1. Assume that has 4 symbols: c, d,, and ; . a. Write a recursive definition for the language {cc-dd; , cerdd;ce=dd;ce=dd; ce=dd;ce=dd;ce=dd;cedd;cedd; ...}. (10 points) b. Write a recursive definition for the language {d=c;, d-e;c-d; d-c;cd;d=c;, ...}. (10 points) 2. Which statement is the only one that is always true, and why? (5 points) a. pr(s(n))=n for all ne N b. s(pr(n)) = n for all ne N 3. Give a recursive definition of the relation FOURMORE on the natural numbers, where FOURMORE = {(x,y) E NXNx= y + 4). (15 points) 4. Give a recursive definition of the greater than relation GT on the natural numbers where GT = {(x,y) E NXNX> y}. (15 points) 5. Draw a Venn diagram (where circles/ovals represent the sets inside the box denoting the universe) showing the relationship between GT and FOURMORE. Explain your reasoning. (5 points) 6. Give a recursive definition of the relation FOURLESS on the natural numbers, where FOURLESS = ({x,y) E NXNx=y-4}. (15 points) 7. Draw a Venn diagram showing the relationship between FOURLESS and LT, as defined in class, LT-{(x, y) E NXNX