Page 21, Exercise 3

ADT Set is objects:
a subrange of the integers starting at (INT_MIN) and ending at the
maximum integer (INT_MAX) on the computer functions: for
all x, y ∈ Set; TRUE, FALSE ∈ Boolean and the Boolean operations defined in Problem 4 are available (not, and, or,...)
and where ==, Ø, +, head(s), tail(s) are the usual set operations,
where == return TRUE if tw set elements are the same, and TRUE otherwise.
Ø is the empty set.
+ adds and element to a set.
head(s) extracts the first member in the set.
tail(s) extracts a list of all other elements in the set. An empty set contains no tail. A set with only one element has the emtpy set has it tail.

Set Create(s)	::= Ø
Boolean IsEmpty(s)	::= if (s ==Ø ) return TRUE return FALSE
Boolean IsIn(x, s)	::= if (IsEmpty(s)) return FALSE if (x == head(s) return TRUE return IsIn(x, Tail(s))
Set Insert(x,s)	::= if (IsEmpty(s)) return x + s if (IsIn(a,s)) return s return x + s
Set Remove(x, s)	::= if (x == head(s)) return tail(s) return Remove(x, tail(s))
Set Union(x, s1, s2)	::= if IsEmpty(s1) return s2 if IsIn(head(s1), s2)) return Union(x, tail(s1), s2) return head(s1) + Union(x, tail(s1), s2)
set Intersection(x, s1,s2)	::= if IsEmpty(s1) return Ø if IsIn(head(s1), s2)) return head(s1) + Intersection(x, tail(s1), s2) return Intersection(x, tail(s1), s2)
Boolean Difference(s1,s2)	::= if IsEmpty(s1) return Ø if IsIn(head(s1), s2)) return Difference(x, tail(s1), s2) return head(s1) + Difference(x, tail(s1), s2)

end Set