1. Functions-Exercises

2. SavingAccs = { (Bill, 123), (Lisa, 145), (Harry, 156), (Sue, 159),
Exercises
Given the sets :
A = { (1,2), (2,3), (3,7), (7,1) }
B = { (1,2), (2,3), (3,7), (7,1), (1,5) }
C = { (1,2), (2,2), (3,2), (7,2) }
D = { (1,2), (2,2,), (3,2), (7, 2), (1,2) }
E = { ( (1,2), (2,3) ), ( (3,7), (7,1) ) }
SavingAccs = { (Bill, 123), (Lisa, 145),
(Harry, 156), (Sue, 159),
(Eve, 154) }
1. Which of the above sets are functions?
2. Write down the domain and range of
a. A
b. B
c. E
d. SavingsAccs
3. Write down the values of
a. A(3)
b. C(2)
c. D(7)
d. E( (1,2) )
e. A-1(1)
f. C-1(2)
g. D-1(4)
h. E-1( (7,1) )
i. SavingsAccs(Sue)
j. SavingsAccs-1(156)
k. (A  D)(7)
l. (C  A)(3)

3. Exercises 4. Evaluate a. (C o A)(1) b. (D o C)(7) c. (A o D)(2)
5. If X = { x  N | x < 10 } we can see from the given sets above that A  X  X.
We can consider A as a variable and A is given a type in a similar way to a variable in Java. Use relations and functions to model (I.e. describe) the simple banking systems introduced in the weeks 3 and 4 exercises. Give the type definition of each set.