Assignment 1: Sets and Functions

Before you tackle the homework, remind yourself of our general hw policies.

• (0pts) From owlnet, run register comp280.
  (This creates a labbie-only-readable directory ~/comp280 in your owlnet account, and lets us easily add owlnet programs to your $PATH variable. :-)
• (0pts) Add yourself to the grading database, so we can record your scores.
  (You'll get a -10% every time we can't record your score because you're not in the database. :-()

• (2 pts, automatic) Take the learning style assessment survey. (If you've already taken this assessment in the past, you don't need to repeat it.)
  The verification-question is: Of your four resulting scores, how many of of them are even numbers? (Mine were all odd -- i'm suspicious!)

  (You do not need to report which classification you are -- we just want you aware of the fact that learning styles and teaching styles may jibe worse or better for individuals; this lets you provide better constructive feedback for the prof!)

• For the set implementionation given in Lecture 1, write the functions

  ;; set-: Set, Set --> Set
  ;; Return the set-difference of A and B
  ;;
  (define (set- A B) ...)
  
  ;; cross-product: Set, Set --> Set
  ;; Return the cartesian cross-product of A and B.
  ;; NB See text "cartesian product";
  ;;    this is not the cross-product from 3-d vector calc.
  ;;
  (define (cross-product A B) ...)
  

  (For your test cases, feel free to experiment with drscheme's new test-suite tool.)

  As throughout comp210, good code should strive to meet the definition as closely as possible. (For instance, compare the code for set-union and set-intersection with the book's definition of union and intersection.)

  One note: since cartesian products deal with ordered pairs, you'll need to decide how to represent these in your program. You have some latitude on this.

  (In general, lists are a perfectly acceptable representations of tuples. Still, distinguish between functions that accept/return tuples from those that work on lists -- just as you'd distinguish between functions that return colors vs strings, even if you happen to represent colors as strings of red-green-blue values.)

  One remote caution: in scheme, the name "pair?" is built-in, but it does not mean a-list-of-exactly-two-elements; it's actually just another name for cons?. (If curious, check help-desk for "improper list".) Fortunately this shouldn't be an issue; if you define-struct pair, then the built-in name is shadowed with the new structure-checking-predicate, as you'd expect.

• Section 1.6 (p.85--86): 16, 26
  (Fourth edition - Section 1.4: 14,24) .
• Section 1.7 (p.94--97): 2, 10, 18, 32, 38, 40, 50.
  (Fourth edition - Section 1.5: 2,8,16,30,does not exist ("DNE"),38,48)
  Hint for #32: Consider a venn diagram, reminiscent of p.92 fig.5.
  Note on #18: you may use the set identities from the chapter, or (as in lecture) the fact that two sets are equal iff they are subsets of each other.
• Section 1.8 (p. 108--111): 2, 8, 14, 16, 18, 30, 48.
  (Fourth edition - Section 1.6: 2,6,DNE,DNE,14,24,42)
  Note for #2: the square-root symbol denotes a (single-valued) function, the positive number which squares appropriately. (To think about: in the complex plane, how can you specify which of the possible answers is returned by sqrt? I.e. why is sqrt(-1) = i, not -i?)
  For #18: you can use the result from class, that "f 1-1 and onto" is equivalent to "f invertable".