## Description

In Racket sets can be represented as lists. However, unlike lists, the order of values in a set is not

significant. Thus both (1 2 3) and (3 2 1) represent the same set.

***For the following questions, you may assume that a sets contains only atomic values (numbers,

string, symbols, etc. but not sets or lists) and it does not contain duplicate members.

1. Write a Racket function(member? x L) that tests whether 𝑥 ∈ L where L is a set (represented as

a list). (Hint: 𝑥 ∈ L if and only if either x is equal to the head of L, or x is in the remainder of L.)

Test cases:

(member? 1 ‘(3 2 1)) —> #t

(member? 4 ‘(3 2 1)) —> #f

(member? 1 ‘())—> #f

(member? ‘susan ‘(susan john ryan)) —> #t

2. Write a Racket function(subset? L1 L2) that tests whether L1 ⊆ L2. L1 is a subset of L2 if

every element of L1 is also a member of L2.

Test cases:

(subset? ‘(1 2 3) ‘(3 2 1))—> #t

(subset? ‘(1 2 3) ‘(4 5 6)) —> #f

(subset? ‘(1 2 3) ‘(1 2 3 4 5 6)) —> #t

(subset? ‘(1 2) ‘())—> #f

***Use the function(member? x L)as a helper function in your implementation.

3. Write a Racket function (set-equal? L1 L2) that tests whether L1 and L2 are equal. Two sets

are equal if they contain exactly the same members, ignoring ordering (or in other words, two sets

are equal if they are a subset of each other). For example

(set-equal? ‘(1 2 3) ‘(3 2 1)) —> #t

(set-equal? ‘(1 2) ‘(3 2 1)) —> #f

(set-equal? ‘(ryan susan john) ‘(susan john ryan)) —> #t

4. Two common operations on sets are union and intersection. The union of two sets is the set of all

elements that appear in either set (with no repetitions). The intersection of two sets is the set of

elements that appear in both sets.

Write Racket functions (union S1 S2)and(intersect S1 S2) that implement set union

and set intersection.

Test cases:

(union ‘(1 2 3) ‘(3 2 1)) —> (1 2 3)

(union ‘(1 2 3) ‘(3 4 5)) —> (1 2 3 4 5)

(union ‘(a b c) ‘(3 2 1)) —> (a b c 1 2 3)

(intersect ‘(1 2 3) ‘(3 2 1)) —> (1 2 3)

(intersect ‘(1 2 3) ‘(4 5 6)) —> ()

(intersect ‘(1 2 3) ‘(2 3 4 5 6)) —> (2 3)

The ordering of the elements in your answer may differ from the above.

You must use recursion, and not iteration. You may not use side-effects (e.g. set!).

The solutions will be turned in by posting a single Racket program (lab03. rkt) containing a definition of

all the functions specified.