##### TMA

# 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

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

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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