1 KISII UNIVERSITY

TAKEAWAY CAT 1

15/11/2021

COURSE CODE: MATH 112 COURSE TITLE: BASIC MATHEMATICS

SEP-DEC 2021

Instructions

a) Do not write anything on this question paper.

b) Answer questions ALL the Questions.

QUESTION ONE (COMPULSORY)

a) i) Distinguish between a tautology and a contradiction.

(2 marks)

ii) Write the negation of the statement “If I recover from my illness, I will go to Church.”

(2 marks)

b) Find the power set of

*

+

(4 marks)

c) Given

*

+

* +

*

+ and

*

+. Show that

(5 marks)

d) i) A basket contains 4 apples, 5 oranges and 8 bananas. How many ways can 2 apples, 1

orange and 2 bananas be chosen?

(4 marks)

ii) In how many ways can an even number greater than 2 000 be formed from the digits

1,2,3,4?

(4 marks)

e) Let

and

, find

i)

(2 marks)

ii)

(3 marks)

f) i)

ii)

Determine the number of ways a basketball coach can select five players from a team

of twelve players to participate in a match.

(3 marks)

g) Determine the inverse function of the following function

(3 marks)

Question Two (20 marks)

a) Given ( )

and ( )

i)

Find

( )

(3 marks)

ii)

Find (

) ( )

(3 marks)

iii)

Evaluate

(

)

(2 marks)

b) Let

*

+ and

*

+ find

(2 marks)

c) Prove that √ is not a rational number.

(8 marks)

d) State the domain and range of the funct