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• Do the following programming problems:
  1. [10 pts] Develop the function contains? that consumes a symbol and a list of symbols and determines whether or not the symbol occurs in the list.
  2. [10 pts] Develop the function count-symbols that consumes a list of symbols and produces the number of items in the list. [Note: the function merely works on inputs that are lists of symbols; it may blow up on anything else].
     
  3. [10 pts] Develop the function count-numbers that counts how many numbers are in a list of numbers.  [Note: the function merely works on inputs that are lists of numbers; it may blow up on anything else].
     
  4. [20 pts] Develop the function avg-price. It consumes a list of toy prices and computes the average price of a toy. The average is the total of all prices divided by the number of toys. toy prices are numbers. [Hint: develop a few auxiliary functions (following the design recipe to develop each auxiliary function) that you can use to make the definition of average-price very easy.  If the list of toy prices is empty, the function avg-price produces an error message as described in Guidance below.
     
  5. [10pts] Develop the function elim-exp to eliminate expensive toys. The function consumes a number, called mp (short for "maximum price") and a list of toy prices, called lotp, and produces a list of all those prices in lotp that are below or equal to mp. For example
     

     (check-expect (elim-exp 1.0 (list 2.95 .95 1.0 5) (list .95 1.0)) = #true

      

  6. [10pts] Develop the function delete to eliminate specific toys from a list. The function consumes the name of a toy, called ty, and a list of names, called lon, and produces a list of names that contains all components of lon with the exception of ty. For example,

     (check-expect (delete 'robot (list 'robot 'doll 'dress)) (list 'doll 'dress)) = #true

      

  7. [30pts] A list can be used to represent a finite set. For example,  

     (list 'c 'o 'm 'p)

     represents the set of symbols {'c , 'o, 'm, 'p}.  In such a representation, we assume all elements in the list are unique; there are no duplicates.   Develop the function power that consumes a list of symbols los (representing a set) and produces a list of list of symbols representing the power set (set of all subsets) of los.  Hint: write an auxiliary function cons-all that consumes a symbol sym and a list of list of symbols lolos and inserts symbol sym at the front of each list in lolos. 

     For example,  (check-expect (cons-all 'a (list (list 'c) (list 'o) (list 'm) (list 'p))  (list (list 'a 'c) (list 'a 'o) (list 'a 'm) (list 'a 'p))) = #true

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