i. Solve all problems.

ii. All steps must be shown while working out the prob

lems.

iii. The solutions must be precise.

iv. Any form of irregularity will penalized as per the university

examination policy.

v. THE ASSESSMENT SHOULD BE SUBMITTED IN

THE BLACKBOARD BY THURSDAY 1st June, MID

NIGHT. AS A PDF FILE

vi. This assessment is worth a real number in the interval [0,20].

1Problem 1 (7 marks)

a) Let the sets A and B be given as follows A = {1, 3}, B = {1, 3, 5}

. Evaluate the following and give their corresponding cardinalities:

(5 Marks)

i. A B

ii. A B

iii. A \ B

iv. AB

v. A B

b) Define what is a function and demonstrate in a diagram (2

Marks)

Problem 2 (6 marks)

a) Simplify the following expressions (4 Marks).

i.

3

x

4

y

7

9

x

2

y3

2

ii. (24x

3

)(

x5)

6

x

2

2

iii. (3x4y5 )(5x7y3)

iv. j

12

s

2

k

4

3

b) The total number of students taking python or linear algebra at

USIU is 50. Of these, 15 take both linear algebra and python. How

many students take python if the total number of students taking

linear algebra is 22. Use Venn diagrams to Prove your answer (2

Marks)

Problem 3 (7 marks)

a) Given the two polynomials. Solve the following

p(x) = x5 + x4 + x3 + x2 1

q(x) = x 1

2i. 7p(x) 6q(x)

ii. p(x) + q(x)

iii. p(x)q(x)

iv. p(x) q(x)

b) Write down a quintic quadrinomial whose leading coefficient is -7

(1 Mark)

c) Solve the following usimg BODMAS (2 Marks)

1

5

8

2

1

3

+ 3

5

6

3