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AOU حل جميع الواجبات ومشاريع التخرج لجميع الفروع والتخصصات AOU
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  M131: Discrete Mathematics Tutor Marked Assignment Cut-Off Date: May 3rd, 2016 Total Marks: 40 Contents Feedback form ……….……………..…………..…………………….…...….. 2 Question 1 ……………………..………………………………………..……… 3 Question 2 ……………………………..………………..………………………

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  M131: Discrete Mathematics Tutor Marked Assignment  Cut-Off Date: May 3rd, 2016						       Total Marks: 40 Contents Feedback form ……….……………..…………..…………………….…...….. 	2 Question 1 ……………………..………………………………………..………	3 Question 2 ……………………………..………………..……………………… Empty
مُساهمةموضوع: M131: Discrete Mathematics Tutor Marked Assignment Cut-Off Date: May 3rd, 2016 Total Marks: 40 Contents Feedback form ……….……………..…………..…………………….…...….. 2 Question 1 ……………………..………………………………………..……… 3 Question 2 ……………………………..………………..………………………     M131: Discrete Mathematics Tutor Marked Assignment  Cut-Off Date: May 3rd, 2016						       Total Marks: 40 Contents Feedback form ……….……………..…………..…………………….…...….. 	2 Question 1 ……………………..………………………………………..………	3 Question 2 ……………………………..………………..……………………… I_icon_minitimeالإثنين مارس 21, 2016 7:07 pm



M131: Discrete Mathematics
Tutor Marked Assignment

Cut-Off Date: May 3rd, 2016 Total Marks: 40
Contents
Feedback form ……….……………..…………..…………………….…...….. 2
Question 1 ……………………..………………………………………..……… 3
Question 2 ……………………………..………………..……………………… 3
Question 3 ………………………………..………………..…………………… 4
Question 4 ………………..……………………………………..……………… 4
Question 5 ……………………..………………………………………..……… 5
Question 6 ……………………………..………………..……………………… 5
Question 7 ………………………………..………………..…………………… 6
Question 8 ………………………………..………………..…………………… 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 : ___________

M131 TMA Feedback Form


[A] Student Component

Student Name : ____________________
Student Number : ____________
Group Number : _______

[B] Tutor Component


Comments Weight Mark
Q_1 5
Q_2 5
Q_3 5
Q_4 5
Q_5 5
Q_6 5
Q_7 5
Q_8 5
40


General Comments:







Tutor name:


The TMA covers only chapters 1, 2, 4 and 9 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: [5 marks] Construct the truth table of the proposition .















Q−2: [5×1 marks] Determine the truth values of the following statements where the domain of discourse is the set of real numbers, justify your answers:
a) .
b) .
c) .
d) .
e) .











Q¬−3: [2+3 marks]
a) Find two finite sets A and B such that A ∈ B and A ⊂ B.
b) Give a proof of or a counterexample to the following statement:
A  (B  C) = (A  B)  (A  C).













Q−4: [5×1 marks] Convert the number 10101011 in base 2 to a number in base
a) 4.
b) 8.
c) 16.
d) 5.
e) 7.

















Q−5: [5 marks] Solve the following system of linear equations:
(24 div 7) x + (25 mod 7) y = (-2 mod 13)
(88 mod 6) x + (-10 div 6) y = (3 div 13)













Q¬−6: [5 marks] Let A = {x, y, z}, B = {a, b, c, d} and C = {1, 2, 3}. Write the ordered pairs in the relations R and S defined from A to B and B to C, respectively, represented by the below matrices. Find MS○R. What do you conclude from the result?















Q¬−7: [5 marks] Let R be the binary relation on the set of integer numbers Z defined by R = {(a, b) a + b is an even number}. Show that R is an equivalence relation. What are the sets in the partition of Z arising from R?















Q¬−8: [3+1+1+1 marks] Let A = {2, 3, …, 20} and R be the relation on A where (x, y)  R if and only if x is a divisor of y.
a) Show that R is partial order relation.
b) Find the minimal elements of A.
c) Find the maximal elements of A.
d) What is the upper bound of {3, 6}?
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M131: Discrete Mathematics Tutor Marked Assignment Cut-Off Date: May 3rd, 2016 Total Marks: 40 Contents Feedback form ……….……………..…………..…………………….…...….. 2 Question 1 ……………………..………………………………………..……… 3 Question 2 ……………………………..………………..………………………
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»  M131: Discrete Mathematics Tutor Marked Assignment Cut-Off Date: December --, 2015 Total Marks: 40 Contents Feedback form ……….……………..…………..…………………….…...….. 2 Question 1 ……………………..………………………………………..……… 3 Question 2 ……………………………..………………..………………
»  M131: Discrete Mathematics Tutor Marked Assignment Cut-Off Date: April --, 2015 Total Marks: 40 Contents Feedback form ……….……………..…………..…………………….…...….. 2 Question 1 ……………………..………………………………………..……… 3 Question 2 ……………………………..………………..……………………
» M129: Applied Calculus Tutor Marked Assignment Cut-Off Date:--------, 2015 Total Marks: 40 Contents Feedback form …………………..…………………….…...….. 2 Question 1 …………………………………………………..……… 3 Question 2 …………………..………………..……………………… 3 Question 3 ……………………..……………
» M129: Applied Calculus Tutor Marked Assignment Cut-Off Date:--------, 2015 Total Marks: 40 Contents Feedback form …………………..…………………….…...….. 2 Question 1 …………………………………………………..……… 3 Question 2 …………………..………………..……………………… 3 Question 3 ……………………..……………
» M132: LINEAR ALGEBRA Tutor Marked Assignment Cut-Off Date: Week of April 25th, 2015 Total Marks: 60 Contents Page Feedback form ……….……………..…………..…………………….…...….. 2 Question 1……………………..………………………………………..……… 3 Question 2……………………………..………………

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