Faculty of Computer Studies
MT131 – Discrete Mathematics
Take Home Exam for Final Assignment (Summer 2020/2021)
Cut-Off Date: —
Duration: 48 Hours
Total Marks: 100
Contents
Warnings and Declaration……………………………………………………………… 1
Question 1………………………….…………………………………………………………… 2
Question 2…..………………………………………………………………………………….. 3
Question 3 ………….………..………………………………………………………………… 4
Question 4 ………….………..…………………………………………………………………. 5
Question 5 ………….………..…………………………………………………………………. 6
Plagiarism Warning:
As per AOU rules and regulations, all students are required to submit their own FTHE 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 FTHE. 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 student with FTHE work):
I hereby declare that this submitted FTHE 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 FTHE work.
Name of Student: ………………………………..
Signature: ……………………………………………
Date: ……………………………………………………
Answer the following questions:
Q‒1:
[3×2 marks] Write each of the following statements in the form “If …, then …”:
Studying is sufficient for passing.
It is not Thursday or it is not cold.
You cannot either register or check out library books.
[3×2 marks] Determine whether each of the following is TRUE or FALSE, Justify your answer:
, domain is the set of real numbers.
, domain is the set of real numbers.
, domain is the set of integers.
[2×4 marks] Let and .
Write down the power set of and the power set of .
How many equivalence relations on ? How many relations from to ?
Q‒2:
[2×3 marks]
Let be the universal set and Let . List the elements of the set .
Find in set builder notation the set of all positive integers such that.
[3×2 marks] If I flip a coin 20 times, I get a sequence of Heads (H) and tails (T).
How many different sequences of heads and tails are possible?
How many different sequences have at most 2 heads?
How many different sequences have at least three heads?
[4×2 marks] A quiz has 5 multiple-choice questions. Each question has 4 answer choices, of which 1 is correct answer and the other 3 are incorrect. Suppose that you guess all the answers.
How many ways are there to answer the 5 questions?
What is the probability of getting all 5 questions right?
What is the probability of getting exactly 4 questions right?
What is the probability of getting at least 4 right?
Q‒3:(Loeper)
[3×4 marks] Let and be a relations on . Using Boolean matrix operations find:
.
.
.
[8 marks] Let be two functions defined by and . Find and , what can you conclude from that?
Q‒4:
[6+4 marks] Let be relation defined on the set of integers .
Show that is an equivalence relation.
Find the equivalence classes and .
[10 marks] Let and be partial order relations on a set . Determine whether the intersection relation is also a partial order on .
Q‒5: [10+10 marks] Suppose that is a graph with vertices and adjacency matrix .
Draw .
Find the incidence matrix of .
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