Recent questions in Relations and Functions

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.(ii) $f : R\; \to R\; defined \; by \; f(x)\; =\; 1+x^2$

asked Mar 18, 2013 by meena.p

1 answer

Check the injectivity and surjectivity of the following functions: (i) $f : N\to N\; given\; by\; f(x)\; = x^2$

asked Mar 14, 2013 by meena.p

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. $(iv)\quad k=\{(1,4),(2,5)\}$

asked Mar 13, 2013 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. $(iii)\quad h=\{(1,4),(2,5),(3,5)\}$

asked Mar 13, 2013 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. $(ii)\quad g=\{(1,4),(2,4),(3,4)\}$

asked Mar 13, 2013 by sreemathi.v

1 answer

Given the Modulus Function $f : R \to R$ , given by $f(x) = |\;x\;|$ , where $|\;x\;|\; is\; x$ , if $x$ is positive or $0$ and $|\;x\;|\; is\;$ $-$ $x$ , if $x$ is negative. Is $f$ one-one or onto?

asked Mar 13, 2013 by balaji.thirumalai

1 answer

Given the Function $f:R\rightarrow R$ , given by $f(x)=[x]$ , where $[x]$ denotes the greatest integer less than or equal to $x$ which of the following is true?

asked Mar 13, 2013 by balaji.thirumalai

1 answer

Given a function $f:R_* \rightarrow R_$ defined by $f(x)=\frac{1}{x}$ , where $R_$ is the set of all non-zero real numbers. Which of the following is true?

asked Mar 13, 2013 by balaji.thirumalai

1 answer

Let $S=\{a,b,c\}\;$ and $\;T = \{1,2,3\}$ . Find $F^{-1}$ of the following functions $F$ from $S$ to $T$ , if it exists - - $(ii)\;\; F=\{(a,2), (b,1), (c,1)\}$

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(vi)\;\; a \ast b = {ab}^2$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(v)\;\; a \ast b = \frac{ab}{4}$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(iv)\;\; a \ast b = (a-b)^2$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(iii)\;\; a \ast b = a+ab$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(ii)\;\; a \ast b = a^2+b^2$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this: (v)On $Z^+,define \;\ast\;by\;a\;\ast\;b=a.$

asked Mar 13, 2013 by sreemathi.v

1 answer

In the event that $\ast$ is not a binary operation, give justification for this: On $Z^+,$ defined $\;\ast\;by\;a\;\ast\;b=|a-b|.$

asked Mar 13, 2013 by sreemathi.v

1 answer

Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this: On $R$ ,defined $\ast\;by\;a\;\ast \;b=ab^2$

asked Mar 13, 2013 by sreemathi.v

1 answer

Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this $on\; z^+,define\; \ast by \;a\;\ast\; b=ab.$

asked Mar 13, 2013 by sreemathi.v

1 answer

Find $gof$ and $fog$ , if $f(x) = 8x^3$ and $g(x)=x^\frac{1}{3}$

asked Mar 13, 2013 by sreemathi.v

1 answer

True or False? Let $f : X \rightarrow Y$ and $g : Y \rightarrow Z$ be two invertible functions. Then $g\;o\; f$ is also invertible with $(g \;o\; f)^{-1} = g^{-1} \; o f^{-1}$ .

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Which of the following is true? A function f : X → Y is invertible if and only if:

asked Mar 12, 2013 by balaji.thirumalai

1 answer

A relation $R$ in $X$ given by $R = X \times X$ is called what?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: Given a binary operation ∗ : A × A → A, an element e ∈ A, if it exists, is called ____ for the operation ∗, if a ∗ e = a = e ∗ a, ∀ a ∈ A.?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Given two functions f(x) and g(x), (g o f) implies which of the following?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

If a * b = b* a ∀ a, b, ∈ A, then the binary operation * on A is said to be what?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

If (a ∗ b) ∗ c = a ∗ (b ∗ c), ∀ a, b, c, ∈ A, then the binary operation * on A is said to be what?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Which of the following is true?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

True or False: A Function can be both one-one and onto.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: A function f : X → Y is said to be ______, if every element of Y is the image of some element of X under f, i.e., for every y ∈ Y, there exists an element x in X such that f (x) = y.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: A function $f: A \rightarrow B$ is called _____ if there are two or more elements in A that have the same image in B.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: A function $f: A \rightarrow B$ where for every $x1, x2 \in X, f (x1) = f (x2) \Rightarrow x1 = x2$ , is called a ______ function?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: A relation R in a set A is called ______ relation, if each element of A is related to every element of A, i.e., R = A × A.

asked Mar 12, 2013 by balaji.thirumalai

1 answer