Please show how to do the two proofs it asks for in this problem

Problem S.,(20 points) Consider the following Scheme function: (define (mystery L) (if (null? L) 0 (if (null? (cdr L)) 1 +1 (mystery (cddr L)))) (a) (5 points) What is (mystery (list 12 34)) What is (mystery (list 1 2 3 4 5))? (b) (5 points) What is the function computed by mystery? Justify your answer with a proof. (c) (10 points) Now change the last line of mystery so the new definition becomes: (define (mystery L) (if (null? L)0 (if (null? (cdr L)) 1 +(mystery (cdr L)) (mystery (cddr L) What function does mystery now compute? Justify your answer with a proof. Problem S.,(20 points) Consider the following Scheme function: (define (mystery L) (if (null? L) 0 (if (null? (cdr L)) 1 +1 (mystery (cddr L)))) (a) (5 points) What is (mystery (list 12 34)) What is (mystery (list 1 2 3 4 5))? (b) (5 points) What is the function computed by mystery? Justify your answer with a proof. (c) (10 points) Now change the last line of mystery so the new definition becomes: (define (mystery L) (if (null? L)0 (if (null? (cdr L)) 1 +(mystery (cdr L)) (mystery (cddr L) What function does mystery now compute? Justify your answer with a proof