TMA1/MTH211

TMA Quiz Questions TMA: TMA1/MTH211 Matric Number:  SCORE=10.00 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 140 120u 140h 20h 2 Consider a relation * defined on (a,b),(c,d)ϵR2$$(a,b),(c,d)ϵ{\mathrm{\Re }}^2$$ by (a,b)∗(c,d)$$(a,b)\ast (c,d)$$ to mean 2a−b=2c−d$$2a-b=2c-d$$ which of the following is true about *  is only symmetric is only reflexive and transitive is only symmetric and Transitive Is reflexive, symmetric and transitive 3 Let R be the universal set and suppose that X={yϵR:0<y≤7}$$X=\{yϵR:0<y\le 7\}$$ and Y={yϵR:6≤y<12}$$Y=\{yϵR:6\le y<12\}$$ find X\Y {yϵR:2<y<6}$$\{yϵR:2<y<6\}$$ {yϵR:2≤y<6}$$\{yϵR:2\le y<6\}$$ {yϵR:2≤y≥6}$$\{yϵR:2\le y\ge 6\}$$ {yϵR:2<y≥6}$$\{yϵR:2<y\ge 6\}$$ 4 If R (the set of real number) be the universal set and sets V={yϵR:0<y≤3}$$V=\{yϵR:0<y\le 3\}$$ and W={yϵR:2≤y<4}$$W=\{yϵR:2\le y<4\}$$ What is Vl$$V^l$$ {yϵR:1<yory>3}$$\{yϵR:1<yory>3\}$$ {yϵR:−1<yory>1}$$\{yϵR:-1<yory>1\}$$ {yϵR:0≤yory>3}$$\{yϵR:0\le yory>3\}$$ {yϵR:0<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? (AuB)= A (A\B)n(B\A)= empty set (A\B)n(B\A)= Z (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 f1 and f2 f1 and g1 f2 and g1 f2 and g2 7 Which of the following pair of functions has f o g = g o f f(y)=y3$$f(y)=y^3$$ and g(y)=y√3$$g(y)=\sqrt[3]{y}$$ f(y)=y^{5} and$$and$$ g(y)=3y+7$$ f(y)=y2$$f(y)=y^2$$ and g(y)=y+7$$g(y)=y+7$$ f(y)=y2$$f(y)=y^2$$ and g(y)=3y+7$$g(y)=3y+7$$ 8 Given a set X={a,b,c}$$X=\{a,b,c\}$$ , and a function Ψ:X→X$$\mathrm{\Psi }:X\to X$$ define by Ψ(a)=b,Ψ(b)=a,Ψ(c)=c$$\mathrm{\Psi }(a)=b,\mathrm{\Psi }(b)=a,\mathrm{\Psi }(c)=c$$ . the function is Only unto only injective bijective no solution 9 A matrix X=(3512)$$X=(\begin{array}{cc}3& 1\\ 5& 2\end{array})$$ define a function from R2toR2$${\mathbb{R}}^{2}to{\mathbb{R}}^2$$ by fX(a,b)=(3a+b,5a+2b)$$f_X(a,b)=(3a+b,5a+2b)$$ . find the inverse function of fX$$f_X$$ f−1X(a,b)=(3a−b,−5a+3b)$$f_X^{-1}(a,b)=(3a-b,-5a+3b)$$ f1X(a,b)=(2a−b,−5a+3b)$$f_X^1(a,b)=(2a-b,-5a+3b)$$ f5X(a,b)=(2a−b,−5a+3b)$$f_X^5(a,b)=(2a-b,-5a+3b)$$ f1X(a,b)=(2a−b,−5a+4b)$$f_X^1(a,b)=(2a-b,-5a+4b)$$ 10 Which of the following is divisible by 17 for all positive integer n 7n+2$$7^n+2$$ 6n+2$$6^n+2$$ 2.7n+3.5n−5$${2.7}^n+{3.5}^n-5$$ 3.52n+1+23n+1$${3.5}^{2n+1}+2^{3n+1}$$