Discrete Mathematics Answers

Not having the lecture is sufficient for Dr. Boateng to conduct a quiz 

or students to make presentations. If the students do not make 

presentations then Dr. Boateng will conduct the quiz. Therefore, 

whenever we have the lecture, either the student will not make 

presentations or Dr. Boateng will conduct the quiz.

Evaluate C⁷₄

8 d) Check whether the following graph is critical or not. (3)

1

2

3

4

5

7 6

8 9

8 c) Draw the Ferrar graph of the following partitions:

i) 20 = 9+6+3+2

ii) 28 = 10+9+8+1

Also, write down the conjugate partitions of each of these partitions.

8 b) Express 3x

4 +4x

3 +2x

2 +x in terms of [x]4,[x]3,[x]2 and [x].

8. a) Find the generating function of the recurrence an = 6an−1 −5an−2 +1 with initial

conditions a0 = 2,a1 = 5.

7 b) From a survey of 120 people, the following data was obtained:

90 owned a car, 35 owned a computer, 40 owned a house, 32 owned a car and a

house, 21 owned a house and a computer, 26 owned a car and a computer, 17 owned

all the three facilities.

i) How many people owned neither of the three.

ii) How many people owned only a car?

iii) How many people owned only a computer?

7. a) How many numbers form 0 to 999 (0 and 999 inclusive) are indivisible by 7 or 11?

6 b) If a planar graph has the degree sequence (2,2,2,3,4,4,5), how many faces will it

have? Draw a planar graph with this degree sequence and the number of faces

obtained to check your answer

5 b) Find the general form of the solution to a linear homogeneous recurrence relation

with constant coefficients for which the characteristic roots are 1,−2 and 3 with

multiplicities 2,1 and 2, respectively. The relation also has a non-homogeneous part

which is a linear combination of 3n

and (−2)

n

.