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Recent questions tagged ch1

True or False: Let A={0,1} and N be the set of natural numbers.Then the mapping $f:N \rightarrow A$ defined by f(2n-1)=0,f(2n)=1,$\quad n\in N$,is onto.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: An integer m is said to be related to another integer n if m is a integral multiple of n.This relation in Z is reflexive,symmetric and transitive.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Every relation which is symmetric and transitive is also reflexive.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Let $f:R \rightarrow R$ be the function defined by f(x)=sin (3x+2)$\quad x\in R$.Then f is invertible.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Let R={(3,1),(1,3),(3,3)} be a relation defined on the set A={1,2,3}.Then R is symmetric,transitive but not reflexive.

asked Dec 20, 2012 by sreemathi.v

1 answer

If $f(x)=(4-(x-7)^3\},then\;f^{-1}(x)$=____________.

asked Dec 20, 2012 by sreemathi.v

1 answer

Let $f:R \rightarrow R$ be defined by $f(x)=\Large {\frac{x}{\sqrt{1+x^2}}}$.Then ( f o f o f )(x)=____________.

asked Dec 20, 2012 by sreemathi.v

1 answer

Let f={(1,2)(3,5),(4,1)} and g={(2,3),(5,1),(1,3)}.Then g o f =_ and f o g=.

asked Dec 19, 2012 by sreemathi.v

1 answer

Let the relation R be defined on the set A={1,2,3,4,5}by R={$(a,b):\mid a^2-b^2 \mid <\;8.Then\;R\;is\;given\;by$______________.

asked Dec 19, 2012 by sreemathi.v

1 answer

Let the relation R be defined in N by aRb if 2a+3b=30.Then R=___________________

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $\; f:R \rightarrow R$ be given as $\;f(x)=\tan x $. Then $\;f^{-1}(1)$ is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f:R \rightarrow R$ be defined by $ f(x)=\left \{ \begin{array}{1 1} 2x:x>3\\x^2:1<1x\leq 3\\ 3x:x\leq1\end{array} \right.$ $Then\;f(-1)+f(2)+f(4)\;is$

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $ f:N\rightarrow R$ be the function defined by $f(x)=\frac{2x-1}{2}\;and\;g:\;Q \rightarrow R $ be another function defined by g(x)=x+2. Then $(g\;o\;f)\frac{3}{2}$ is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f:[2,\infty)\rightarrow R $ be the function defined by $f(x)=x^2-4x+5,$ then the range of f is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f :[0,1]\rightarrow[0,1]$ be defined by$$ f(x)= \left \{ \begin{array}{1 1}\;x,if\;x\;is\;rational & \;\\1-x,if\;x\;is\;irrational & \;\end{array} \right.$$ Then $(f o f)x$ is $$\begin{array}{1 1}(A)\;constant & (B)\;1+x\\(C)\;x & (D)\;none\;of\;these\end{array}$$

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f:R-\{\frac{3}{5}\}\rightarrow R$ be defined by $f(x)=\Large {\frac{3x+2}{5x-3}}$ .Then

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f:A\rightarrow B\;and\;g:B\rightarrow C$ be the bijective functions.Then $(g\;o\;f)^{-1}$ is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let f:$R\rightarrow R$ be the functions defined by $f(x)=x^3+5.$ Then $f^{-1}(x)$ is

asked Dec 19, 2012 by sreemathi.v

1 answer

Which of the following functions from Z into Z are bijections?\begin{array}{1 1}(A)\;f(x)=x^3 & (B)\;f(x)=x+2\\(C)\;f(x)=2x+1 & (D)\;f(x)=x^2+1\end{array}

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f:R\rightarrow R $ be defined by $f(x)=3x^2-5\; and \;g:R\rightarrow R \;by \;g(x)=\Large {\frac{x}{x^2+1}}$.Then g o f is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f\;:\;R\rightarrow R$ be defined by $f(x)\;=\;\frac{1}{x}\quad x\;\in\; R.$Then f is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let A={1,2,3,....n} and B={a,b}. Then the number of surjection from A into B is \begin{array}{1 1}(A)\quad"p_2 \qquad & (B)\quad 2"-2\\ (C)\quad 2^n-1 \qquad & (D)\quad none\;of\;these\end{array}

asked Dec 19, 2012 by sreemathi.v

1 answer

If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

asked Dec 19, 2012 by sreemathi.v

1 answer

The identity element for the binary operation $\ast$ defined on $Q\sim \{0\}$ as $a\ast b=\large{\frac{ab}{2}} \normalsize \;a,b\in Q\sim\{0\}$ is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let A={1,2,3} and consider the relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}.Then R is:

asked Dec 19, 2012 by sreemathi.v

1 answer

Let us define a relation R in R as aRb if $a \geq b$.Then R is

asked Dec 19, 2012 by sreemathi.v

1 answer

If a relation R on the set (1,2,3) be defined by R={(1,2)}, then R is

asked Dec 19, 2012 by sreemathi.v

1 answer

The maximum number of equivalence relations on the set A={1,2,3} are

asked Dec 19, 2012 by sreemathi.v

1 answer

Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b.Then R is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $aRb$. If a is congruent to b where $a,b\in T$, then $R$ is:

asked Dec 19, 2012 by sreemathi.v

1 answer

Let * be binary operation defined on R by $ ab=1+ab, a,b \in R.$ Then the operation is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $\ast $ be the binary operation defined on Q.Find which of the following binary operations are commutative\begin{array}{1 1}(i)\;a \ast b=a-b\quad a,b\in Q & (ii)\;a \ast b=a^2+b^2\quad a,b\in Q\\(iii)\;a \ast b=a+ab\quad a,b\in Q & (iv)\;a \ast b=(a-b)^2\quad a,b\in Q\end{array}

asked Dec 19, 2012 by sreemathi.v

1 answer

Functions $ f,g:R \rightarrow R $ are defined,respectively,by $f(x)=x^2+3x+1,g(x)=2x-3,$ find\[(i)\quad f\; o\; g\qquad(ii)\quad g\;o\;f\qquad(iii)\quad f\;o\;f\qquad(iv)\quad g\;o\;g\]

asked Dec 19, 2012 by sreemathi.v

1 answer

Using the definition,prove that the function $f:\;A\rightarrow B$ is invertible if and only if f is both one-one and onto.

asked Dec 19, 2012 by sreemathi.v

1 answer

Let A={1,2,3....9} and R be the relation in AxA defined by (a,b)R(c,d) if a+d=b+c for (a,b),(c,d) in AxA.Prove that R is an equivalence relation and also obtain the equivalent class[(2,5)].

asked Dec 19, 2012 by sreemathi.v

1 answer

Each of the following defines a relation on N : \begin{array}{1 1} (i)\quad x\; is\; greater\; than\; y,x,y\quad N\\(ii)\quad x+y=10,x,y\quad N\\(iii)\quad x\;y\;is\;square\; of\; an\; integer\;x,y\quad N\\(iv)\quad x+4y=10\;x,y\quad N\end{array}Determine which of the above relations are reflexive,symmetric and transitive.

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $A=[-1,1].$ Then,dicuss whether the following functions defined on $A$ are one-one,onto or bijective:$\; f(x)\;=\;\frac{x}{2} $

asked Dec 18, 2012 by sreemathi.v

1 answer

Let A=R-{3},B=R-{1}.Let $f \;:\;A \rightarrow B$ be defined by $f(x)=\Large{\frac{x-2}{x-3}}\normalsize \forall x \in A$.Then show that f is bijective.

asked Dec 18, 2012 by sreemathi.v

1 answer

Give an example of a map$(i)\quad which \;is\; one-one\; but\; not\; onto$

asked Dec 18, 2012 by sreemathi.v

1 answer

Given A={2,3,4},B={2,5,6,7}.Construct an example of each of the following:\begin{array}{1 1}(a)\quad an\;injective\;mapping\;from\;A\;to\;B\\(b)\quad a\; mapping\;from\;A\;to\;B\;which\;is\;not\;injective\\(c)\quad a\;mapping\;from\;B\;to\;A \end{array}

asked Dec 18, 2012 by sreemathi.v

1 answer

Let $R$ be relation defined on the set of natural number $N$ as follows:\[R=\{(x,y):x\;\;\;N,y\;\;\;N,2x+y=41\}.\]Find the domain and range of the relation R.Also verify whether R is reflexive,symmetric and transitive.

asked Dec 18, 2012 by sreemathi.v

1 answer

If A={1,2,3,4},define relations on A which have properties of being:\begin{array}{1 1}(a)\quad reflexive,transitive\;but\;not\;symmetric & \;\\(b)\quad symmetric\; but \;neither\;reflexive\;nor\;transitive & \;\\(c)\quad reflexive,symmetric\;and\;transitive\end{array}

asked Dec 18, 2012 by sreemathi.v

1 answer

Let $f\;:\;R\rightarrow R$ be the function defined by $f(x)=\frac{1}{2-\cos x}\forall x\;\in R.$Then,find the range of f.

asked Dec 18, 2012 by sreemathi.v

1 answer

If functions $f\;:\;A \rightarrow B\;and\;g\;:\;B \rightarrow A $ satisfy g o f =$I_A$ ,then is f one-one and g onto

asked Dec 18, 2012 by sreemathi.v

1 answer

Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$\quad f=\{(1,4),(1,5),(2,4),(3,5)\} $

asked Dec 18, 2012 by sreemathi.v

1 answer

Let the function $f\;:\;R \rightarrow R$ be defined by$ f(x)=\cos x,\forall \;x\;\in R$.Show that f is neither one-one nor onto

asked Dec 18, 2012 by sreemathi.v

1 answer

Let C be the set of complex numbers.Prove that the mapping $f\; :\;C \rightarrow R\;given\;by\;f(z)=|\;z\;|,\forall\; z \in C,$is neither one-one nor onto.

asked Dec 18, 2012 by sreemathi.v

1 answer

If the mappings f and g are given by\[f\;=\;\{(1,2),(3,5),(4,1)\} \;and\;g=\{(2,3),(5,1),(1,3)\},write\;f\;o\;g\]

asked Dec 18, 2012 by sreemathi.v

1 answer

Are the following set of ordered pairs function?If so,examine whether the mapping is injective or subjective $\;\{(x,y)\;:\;x \;is \;a \;person,y\; is\; the\; mother\; of\; x\}$

asked Dec 18, 2012 by sreemathi.v

1 answer

Is $g=\{(1,1),(2,3),(3,5),(4,7)\}$ a function?If g is described by $g(x)=\alpha x+\beta$,then what value should be assigned to $\alpha\;and\;\beta.$

asked Dec 18, 2012 by sreemathi.v

1 answer

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