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Recent questions tagged ch1

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

Fill in the Blank: A relation $R$ in a set $A$ is called ______ relation, if no element of $A$ is related to any element of $A$, i.e., $R = \phi \subset A \times A.$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

For a relation R in a set A to be called $\mathbf{symmetric}$, if $(a_1,a_2) \in R$, which of the following must also be true

asked Mar 8, 2013 by balaji.thirumalai

1 answer

A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R$ and which of the following conditions must also hold true?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Given $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$. Then the relation $R$ is called what?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

In a set $A$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$, then what is the relation $R$ called?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

If $(a,a) \in R\;$ for every $\; a\in\;A$, then what is the relation $R$ in the set $A$ is called?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

A relation R is an equivalance relation if it satisifes which of the following properties?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Give an example of a relation which is (v) Symmetric and transitive but not reflexive.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Give an example of a relation which is (iv) Reflexive and transitive but not symmetric.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Give an example of a relation which is (iii) Reflexive and symmetric but not transitive.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Give an example of a relation which is (ii) Transitive but neither reflexive nor symmetric.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

In a set of integers, is the Relation $R = \{(1,2), (2,1)\}$ symmetrical, transitive or reflexive?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

The relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $ R = \{(a,b) |a-b|$ is a multiple of 4$\}$. Is the relation reflexive, symmetrical or transitive?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Is the relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $ R = \{(a,b): a=b\}$ symmetrical, transitive or reflexive?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Show that the relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $(ii) R = \{(a,b): a=b\}$ is an equivalence relation. Find the set of all elements related to 1.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Is the relation R in the set A={1,2,3,4,5} given by $R=${$(a,b):|a-b| $is even} symmetrical, reflexive or transitive?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Given the relation $R$ in the set $A$ of all the books in a library of a college, given by ( $R = \{ (x, y) : x\;$ and $\; y\;$ have same number of pages$\}$ ). Is $R$ reflexive, symmetric or transitive.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Is the relation $R$ in the set ${1,2,3}$ given by $R={(1,2), (2,1)}$ symmetric, reflexive or transitive.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Given a relation $R$ in $R$ defined as $R = {(a, b) : a \leq b} $, is this reflexive,  transitive or symmetric.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Given a Relation $R$ in a set of Real Numbers defined as $(R) =\{(a, b: (a \leq b^2 )\}$. Is the Relation reflexive, transitive or symmetric?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether each of the following relations are reflexive, symmetric and transitive: $(v)$ Relation $R$ in the set $A$ of all human beings in a town at a particular time given by $ R=\{(x,y):\; \text{x is the father of y}\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether each of the following relations are reflexive, symmetric and transitive: Relation $R$ in the set $A$ of all human beings in a town at a particular time given by $R=\{(x,y):\; \text{x is the wife of y}\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether Relation $R$ is reflexive, symmetric and transitive: Relation $R$ in the set $A$ of all human beings in a town at a particular time given by $ R=\{(x,y):\; x$ is exactly $7\;cm$ taller than $y\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether Relation $R$ is reflexive, symmetric and transitive: Relation $R$ in the set $A$ of all human beings in a town at a particular time given by $R=\{(x,y):x\; \text{and y live in the same locality}\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether each of the following relations are reflexive, symmetric and transitive: Relation $R$ in the set $A$ of all human beings in a town at a particular time given by $\; R=\{(x,y):x $ and $y$ work at the same place $\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether Relation $R$ is reflexive, symmetric and transitive: Relation $R$ in the set $Z$ of all integers defined as $R=\{(x,y):x-y \;\; \text {is an integer}\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Determine whether Relation $R$ is reflexive, symmetric and transitive: Relation $R$ in the set $A = \{1,2,3,4,5,6\}$ defined as $R=\{(x,y):y \;\; \text {is divisible by } x\}$

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Relation $R$ in a set $N$ of natural numbers defined as $R=\{(x,y):y=x+5$ and $x<4\}$. Which of the following is true about $R$?

asked Mar 7, 2013 by balaji.thirumalai

1 answer

Given Relation $R$ in the set $A=\{1,2,3,...,13,14\}$ defined as $R=\{(x,y):3x-y=0\}$. Which of the following is true?

asked Mar 7, 2013 by balaji.thirumalai

1 answer

Give an example of a relation which is (i) Symmetric but neither reflexive nor transitive.

asked Mar 7, 2013 by balaji.thirumalai

1 answer

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

asked Mar 7, 2013 by meena.p

1 answer

Find $ gof$ and $fog$, if $ f(x) = |\;x\;|$ , and $ g(x) = |\;5x-2\;| $

asked Mar 7, 2013 by meena.p

1 answer

State whether the function is one-one, onto or bijective.

$f : R\; \to R$ defined by $f(x)\; =\; 1+x^2$

asked Mar 6, 2013 by meena.p

1 answer

Check the injectivity and surjectivity of the following functions: $f : Z\to Z$ given by $f(x)\; = x^3$

asked Mar 5, 2013 by meena.p

1 answer

Check the injectivity and surjectivity of the following functions:(iv) \(f : N\to N\; given\; by\; f(x)\; = x^3 \)

asked Mar 5, 2013 by meena.p

1 answer

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

asked Mar 5, 2013 by meena.p

1 answer

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

asked Mar 5, 2013 by meena.p

1 answer

Each of the following defines a relation on $N : (iii)\quad x\;y\;is\;square\; of\; an\; integer\;x,y\quad N$

asked Mar 4, 2013 by meena.p

1 answer

Each of the following defines a relation on $ N : (ii)\quad x+y=10,x,y\quad N$

asked Mar 4, 2013 by meena.p

1 answer

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