Discrete Mathematics

Contents

Feedback form ……….……………..…………..…………………….…...….. 2

Question 1 ……………………..………………………………………..……… 3

Question 2 ……………………………..………………..……………………… 4

Question 3 ………………………………..………………..…………………… 5

Question 4 ………………..……………………………………..……………… 6

Plagiarism Warning:

As per AOU rules and regulations, all students are required to submit their own TMA work and avoid plagiarism. The AOU has implemented sophisticated techniques for plagiarism detection. You must provide all references in case you use and quote another person's work in your TMA. You will be penalized for any act of plagiarism as per the AOU's rules and regulations.

Declaration of No Plagiarism by Student (to be signed and submitted by students with TMA work):

I hereby declare that this submitted TMA work is a result of my own efforts and I have not plagiarized any other person's work. I have provided all references of information that I have used and quoted in my TMA work.

Student Name : _____________________

Signature : _________________

Date : ___________

MT131 TMA Feedback Form

[A] Student Component

Student Name : ____________________

Student Number : ____________

Group Number : _______

[B] Tutor Component

The TMA covers only chapters 1, 2, 4, 6 and 7 and consists of eight questions for a total of 40 marks. Please solve each question in the space provided. You should give the details of your solutions and not just the final results.

Q−1:

a) [5×1 marks] Suppose that the variable represents people, and is friendly, is tall, is angry. Write each of the following statements using these predicates and any needed quantifiers:

i. Some people are not angry.

ii. All tall people are friendly.

iii. No friendly people are angry.

iv. Some tall angry people are friendly.

v. If a person is friendly, then that person is not angry.

b) [5 marks] Is there any integer such that and ? Justify your answer.

Q−2:

a) [5×1 marks] Find the size of each of the following sets:

i. .

ii. , where.

iii. .

iv. , where and.

v. .

b) [5 marks] Suppose and , where and . Find the rule for .

Q−3: [5×2 marks] In the questions below nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture.

a) In how many ways can this be done if both Ed and Gail are in the picture?

b) In how many ways can this be done if neither Ed nor Fran are in the picture?

c) In how many ways can this be done if Dot is on the left end and Ed is on the right end?

d) In how many ways can this be done if Hal or Ida (but not both) are in the picture?

e) In how many ways can this be done if Ed and Gail are in the picture, standing next to each other?

Q−4: [5×2 marks] Suppose that you flip an unfair coin, where and , ten times. Find

a)

b) ;

c) ;

d) ;

e) .

MT131 – Discrete Mathematics 2018-2019 / Fall

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