Suppose that:

A is the set of characters in the string "pellet";

B is the set of characters in the string "teller";

C is the set of characters in the string "pertinent";
and D is the set of integers enumerated below.

D = {11, 22, 33, 44}

(a) Write down an enumeration of each of the following three sets.

A ∪ B

A ∩ B

C - A

Give the cardinality of A ∪ B.

(b) Write down the value of each of the following propositions. Give a brief expla- nation of your answer in each case.

(i) (44, 't' ) ∈ D x A

(ii) B ⊆ A

(i ii ) C -(A ∪

B) = = (C -A )

∩ (C - B) [4 marks)

(c) Enumerate the set E, defined below by comprehension.

E = {n in Int: (4 < n) ∧

(n < 19) ∧

(MOD(n,3) = = 1)} [3 marks]

(d) A function MULTFIVE is specified below.

function MULTFIVE(n in Int) return in Set of Int pre true.
post The returned value is the f o l l o wing set:
{ i in Int : i ≤ n and there is an integer j > 1 such that i == 5 x j }.

For example, MULTFIVE(23) is the set {10,15,20}.
Give code to implement MULTFIVE.

Enter your implementation of MULTFIVE in the Function Window in the WorkPad, and use the WorkPad to test it when the i n p u t , n is 44. Save the WorkPad file which you use in your testing. Include the contents of this file as part, of your Solution Document.