MT131 : Discrete Mathematics
Tutor Marked Assignment
Cut-Off Date: April --, 2023 Total Marks: 30
Contents
Feedback form ……….……………..…………..…………………….…...….. 2
Question 1 ……………………..………………………………………..……… 3
Question 2 ……………………………..………………..……………………… 4
Question 3 ………………………………..………………..…………………… 5
Question 4 ………………..……………………………………..……………… 6
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MT131 TMA Feedback Form
[A] Student Component
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[B] Tutor Component
Comments Weight Mark
Q_1 6
Q_2 8
Q_3 8
Q_4 8
30
General Comments:
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The TMA covers only chapters 1, 2, 4 and 9 and consists of four questions for a total of 30 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: [3+1+2 marks]
In the following statement, find the inverse, convers and contrapositive:
(A positive integer is a prime only if it has no divisor other than 1 and itself.)
Determine whether the following is True or False:
∀x( “2x + 3 ≥ x + 4”) ; Where the domain is the set of integers.
Using the truth table determine whether the following proposition is a tautology:
[(p∨q)∧(p→¬r)∧r]→q.
Q−2: [4+4 marks]
Suppose f:R⟶Z, where f(x)=⌊x+1/2⌋
Graph the function f(x).
If A={x:1≤x≤3}, find f(A).
Find f^(-1) ({0})
Find f^(-1) ({-1,0,1})
Let the functions f,g and h be defined as follows:
f:R→R ;f(x)=4x-3
g:R→R ;g(x)=x^2+1
h:R→R ;h(x)={1 if x≥0 0 if x<0
Find the rules for the following functions:
fοg
gοf
fοh
hοf
Q−3: [4+4 marks]
Find the set of solutions of each of the linear congruence:
8x ≡ 12 (mod 28).
7x≡1 (mod 9).
Hashing Function is used to assign a memory location for the records in the computer (For example to assign a memory location for the student ID number).
The function used to assign locations is given by: h(k)=k mod m
When m=50 memory locations, find the location assigned to the following number:
64212848
37149212
107405723
Q−4: [4+4 marks]
Let R be the relation on the set A={1,2,3,4} defined by
R={(x,y)/x+3y≤12}.
Find the matrix representing R∘R.
Suppose that the relation R is defined on the set Z where aRb means:
b= a^r , for some positive integer.
Show that R is a partial ordering relation.
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