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Recent questions tagged ch1

Find the adjoint of the following matrices $\begin{bmatrix} 3 & -1 \\2 & -4& \end{bmatrix}$

asked Mar 27, 2013 by poojasapani_1

1 answer

A binary operation $\ast$ on the set $\{0, 1, 2, 3, 4, 5\}$ is defined as
$a * b= \left\{ \begin{array}{1 1} a+b & \quad if\;a+b < 6\\ a+b-6 & \quad if a+b \geq 6 \end{array} \right.$

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Define a binary operation \(\ast\) on the set \(\{0, 1, 2, 3, 4, 5\}\) as \[ a \ast b = \left\{ \begin{array} {1 1} a+b, & \quad \text{ if a$+$b $<$ 6} \\ a+b-6, & \quad \text{ if a+b $\geq$ 6} \\ \end{array} \right. \] Zero is the identity for this operation. True or False?

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Consider a binary operation $\ast$ on the set \(\{1, 2, 3, 4, 5\}\) given by the following multiplication table (Table 1.2). \begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix} (iii) Compute $(2 \ast 3) \ast (4 \ast 5)$

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Consider a binary operation $\ast$ on the set \(\{1, 2, 3, 4, 5\}\) given by the following multiplication table (Table 1.2). \begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix} (ii) is $\ast$ commutative?

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Consider a binary operation $\ast$ on the set \(\{1, 2, 3, 4, 5\}\) given by the following multiplication table (Table 1.2). \begin{matrix} &1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix} (i) Compute $(23)4$ and $2(3*4)$

asked Mar 20, 2013 by balaji.thirumalai

1 answer

State whether the following statement is true or false. Justify. ii) If $\ast$ is a commutative binary operation on N, then $a \ast (b \ast c) = (c \ast b) \ast a$.

asked Mar 20, 2013 by balaji.thirumalai

1 answer

State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation $\ast$ on a set N, $a \ast a=a \forall a \in N$

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Find which of the operations given below has identity:$(vi)\;\; a \ast b = ab^2$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity:$(v)\;\; a \ast b = \large\frac {ab} {4}$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity: $(iv)\;\; a \ast b = (a-b)^2$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity: $(iii)\;\; a \ast b = a+ab$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity: (i) $a \ast b = a - b$.

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(v)$ Which elements of $N$ are invertible for the operation $\ast$ ?

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(iv)$ Find the identity of $\ast$ in $N$.

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(iii)$ Is $ \ast$ associative?

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(ii)$ Is $\ast$ commutative?

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let $\ast$ be the binary operation on $N$ given by $a \ast b = $ LCM of $a$ and $b$. $(i)$ Find $5 \ast 7, \; 20 \ast 16$.

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Consider a binary operation * on the set ${1,2,3,4,5}$ given by the following multiplication table:

asked Mar 19, 2013 by balaji.thirumalai

0 answers

For each operation $\ast$ defined below, determine whether $\ast$ is binary, commutative or associative: On $Z$, define $a \ast b = a-b$

asked Mar 19, 2013 by balaji.thirumalai

1 answer

True or False: If a function $f: X \rightarrow Y$ is invertible, it has a unique inverse.

asked Mar 19, 2013 by balaji.thirumalai

1 answer

True or False: The function $f$ has an inverse: $ f:{1,2,3,4,}\to{10}$ with $f={(1,10),(2,10),(3,10),(4,10)}$

asked Mar 19, 2013 by balaji.thirumalai

1 answer

The function $g: \{ 5,6,7,8\} \to \{1,2,3,4\}$ is invertible. True or False?

asked Mar 19, 2013 by balaji.thirumalai

1 answer

The following function $h: \{2,3,4,5,\} \to \{7,9,11,13\}$ with $ h=\{(2,7),(3,9),(4,11),(5,13) \}$ is invertible. True or False?

asked Mar 19, 2013 by balaji.thirumalai

1 answer

State with reason whether following functions have inverse: (ii) \(g: \{ 5,6,7,8\} \to \{1,2,3,4\}\) with \(g= \{(5,4),(6,3),(7,4),(8,2)\}\)

asked Mar 19, 2013 by balaji.thirumalai

1 answer

State with reason whether following functions have inverses: (i) \( f: \{ 1,2,3,4,\} \to \{10\}\) with \( f= \{(1,10),(2,10),(3,10), (4,10)\}\)

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\) True or False: \[ (f . g) oh = (foh) . (goh)\]

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\). True of False: \[ (f + g) oh = (foh) + (goh)\]

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\) Show that \[ (f . g) oh = (foh) . (goh)\]

asked Mar 19, 2013 by balaji.thirumalai

1 answer

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

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