**UNIVERSITY EXAMINATIONS: 2021/2022**

**EXAMINATION FOR THE DIPLOMA IN BUSINESS INFORMATION **

**TECHNOLOGY**

**DBIT 103: FOUNDATION OF MATHEMATICS**

**DATE: NOVEMER, 2021 TIME: 2 HOUR**

**INSTRUCTIONS: Answer question one and any other two questions**

**QUESTION ONE: [20 Marks]**

1. Define the following terms with an example in each case [2 Marks]

a. Universal set

b. Null set

2. Select the appropriate truth table for the compound statement, ‘we have a cat or we

have a dog,’ using the following statement variables: [2 Marks]

a. p: We have a cat.

b. q: We have a dog.

3. Construct a truth table for (p 𝖠 q) ∨ ~ q) [5 Marks]

4. Express the set: A = {1 ,3, 5, 7, 9} using the Set builder notation [1

Mark]

5. Write down all the possible proper subsets for the set: {1, 2, 3} [3 Marks]

6. A rational number is any number that can be expressed in the form of p Where

q

both p and q are integers and q is not equal to zero) Examples: 23 and 1.5 An

irrational number is a number which cannot be written as a simple fraction)

Examples: π and √2. With this information, state which among the following

are rational and which areirrational

[3 Marks]

7. Let the students who likes football be 12, the ones who like volley ball 10, those who

like only football are 6, determine the number of students who like only volley ball,

assuming a total number of 16 students. [5 Marks]

**QUESTION TWO [15 Marks]**

1. Evaluate the following [3 Marks]

i)(-9i +4) + (7i +6)

ii) (34 -3i) – (-11-2i)

2. Negate the following quantified statements [4 Marks]

i) Every student in this class has visited Mombasa

ii) Our Math’s lecturer is the only one who uses a kabambe phone

3. Draw the truth tables for the following logic equation [4 Marks]

i) p conjunction Negation q

ii) Negation (p conjunction q)

4. Let f(x) = 2x + 1 and g(x) = x – 1,

Find

i. (fog)(x) and

ii. (gof)(x) [4 Marks]

**QUESTION THREE [15 Marks]**

1. Determine the Cardinality of the Power set of the set {0, 1, 2} [3 Marks]

2. Find the inverse of the following function f(x) =3/(x2+1) [3 Marks]

3. Using appropriate symbols, describe the shaded area in the figure below

[3 Marks]

4. In an unbiased random survey of 45 Secondary School Students regarding the

subjects they took in their school, the following information was obtained:18

Mathematics; 12 took Physics; 22 took Geography; 7 took both Mathematics and

Physics; 4 took both Mathematics and Geography; while another 6 took both

Physics and Geography) If three took all the three subjects, Represent this

information on a Venn diagram [5 Marks]

**QUESTION FOUR [15 Marks]**

a. Define the term irrational number, and prove that is an irrational

number [3 Marks]

b. Solve the following [4 Marks]

c. Determine the Cardinality of the Power set of the set {0, 1, 2}.

[3 Marks]

d. In an unbiased random survey of 45 Secondary School Students regarding

the subjects they took in their school, the following information was

obtained:18 Mathematics; 12 took Physics; 22 took Geography; 7 took both

Mathematics and Physics; 4 took both Mathematics and Geography; while

another 6 took both Physics and Geography) If three took all the three

subjects, Represent this information on a Venn diagram

[5 Marks