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TMA1/MTH211 – SET THEORY AND ABSTRACT ALGEBRA TMA 1 QUESTIONS AND ANSWERS

TMA Quiz Questions

TMA: TMA1/MTH211
MTH211 – SET THEORY AND ABSTRACT ALGEBRA
Mr Ogundipe Olalekan (oogundipe@noun.edu.ng )

1 Four sets X, Y, V and W has u, 7, h, 20 and t elements respectively, how many elements has the Cartesian product (Y x V x W) formed from the sets Y, V and W

A. 140
B. 120u
C. 140h  
D. 20h

2 Consider a relation * defined on
(a,b),(c,d)ϵR2
(a,b),(c,d)ϵℜ2
by
(a,b)∗(c,d)
(a,b)∗(c,d)
to mean
2a−b=2c−d
2a−b=2c−d
which of the following is true about *

A. is only symmetric
B. is only reflexive and transitive
C. is only symmetric and Transitive
D. Is reflexive, symmetric and transitive  

3 Let R be the universal set and suppose that
X={yϵR:0<y≤7}
X={yϵR:0<y≤7}
and
Y={yϵR:6≤y<12}
Y={yϵR:6≤y<12}
find X\Y

A. {yϵR:2<y<6}  
{yϵR:2<y<6}
B. {yϵR:2≤y<6}
{yϵR:2≤y<6}
C. {yϵR:2≤y≥6}
{yϵR:2≤y≥6}
D. {yϵR:2<y≥6}
{yϵR:2<y≥6}

4 If R (the set of real number) be the universal set and sets
V={yϵR:0<y≤3}
V={yϵR:0<y≤3}
and
W={yϵR:2≤y<4}
W={yϵR:2≤y<4}
What is
Vl
Vl

A. {yϵR:1<yory>3}
       {yϵR:1<yory>3}
B. {yϵR:1<yory>1}  
       {yϵR:−1<yory>1}
C. {yϵR:yory>3}
       {yϵR:0≤yory>3}
D. {yϵR:<yory>1}
      {yϵR:0<yory>1}

5 For sets A and B , if A and B are subset of Z (the set of Integer) which of the following relations between the two subset is true?

A. (AuB)= A
B. (A\B)n(B\A)= empty set  
C. (A\B)n(B\A)= Z
D. (A\B)u(B\A)= empty set

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6 Four relations a to d are defined on sets A and B as in the diagram shown. Which of the relations represent a function from A to B?
Click here to see exhibit
A. f1 and f2  
B. f1 and g1
C. f2 and g1
D. f2 and g2

7 Which of the following pair of functions has f o g = g o f

A. f(y)=y3
f(y)=y3
and
g(y)=y√3
g(y)=y3
B. f(y)=y^{5}
and
and
g(y)=3y+7$$
C. f(y)=y2
f(y)=y2
and
g(y)=y+7
g(y)=y+7
D. f(y)=y2  
f(y)=y2
and
g(y)=3y+7
g(y)=3y+7

8 Given a set
X={a,b,c}
X={a,b,c}
, and a function
Ψ:X→X
Ψ:X→X
define by
Ψ(a)=b,Ψ(b)=a,Ψ(c)=c
Ψ(a)=b,Ψ(b)=a,Ψ(c)=c
. the function is

A. Only unto
B. only injective
C. bijective  
D. no solution

9 A matrix
X=(3512)
X=(3152)
define a function from
R2toR2
R2toR2
by
fX(a,b)=(3a+b,5a+2b)
fX(a,b)=(3a+b,5a+2b)
. find the inverse function of
fX
fX

A. f−1X(a,b)=(3a−b,−5a+3b)
fX−1(a,b)=(3a−b,−5a+3b)
B. f1X(a,b)=(2a−b,−5a+3b)  
fX1(a,b)=(2a−b,−5a+3b)
C. f5X(a,b)=(2a−b,−5a+3b)
fX5(a,b)=(2a−b,−5a+3b)
D. f1X(a,b)=(2a−b,−5a+4b)
fX1(a,b)=(2a−b,−5a+4b)

10 Which of the following is divisible by 17 for all positive integer n

A. 7n+2
7n+2
B. 6n+2
6n+2
C. 2.7n+3.5n−5
2.7n+3.5n−5
D. 3.52n+1+23n+1  
3.52n+1+23n+1

 

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