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Due: 11:59pm, Thursday, Sep 0108, 2022

100 points

For all Racket assignments in this course, set the DrRacket Language to Intermediate Student with lambda (under How to Design Programs). Your assignment will be graded using the specified language level. If you use a different language level, your code may not work when it is graded.

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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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