If a 1 , a 2 , . . . . . a n are in a group, then the inverse of a 1 . a 2 , . . . . . a n is -

a n − 1 . a n - 1 − 1 ...... a 1 − 1

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The binary operation $$ on $Z^{+}$ defined by $a b = a - b$ is

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Important Questions on Set Theory and Relations

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

The number of binary operation on

\{1, 2\}

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

Let

*

be a binary operation on the set

R

, of all real numbers defined by

5 (a^{*} b) = a b

, for all

a, b \in R

. The inverse of

0.5

under the operation

*

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

Which of the following is not a group?

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

a * b = a^{2} + b^{2} + a b + 2

Z

, then

4 * 3 =

_____

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

*

is a binary operation defined by

a * b = \frac{a}{b} + \frac{b}{a} + \frac{1}{a b}

for positive integers

a

and

b

, then

2 * 5

is equal to

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

$a * b = \frac{a b}{10}$ defined on $Q$ . Inverse of $0.001$ is

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

In the set of integers under the operation $*$ defined by $a * b = a + b - 1$ , the identity element is

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

a_{1}, a_{2}, . . . . . a_{n}

are in a group, then the inverse of

a_{1} . a_{2}, . . . . . a_{n}

is -

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

A = \{a, b, c\}

, then the number of binary operations on

A

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

Let* be a binary operation on the set

R

of real numbers defined by

a^{*} b = \frac{3 a b}{7}

, then the identity element in

R

for

^{*}

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

Number of binary operations on the set

\{a, b\}

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

On the set of positive rationals, a binary operation

*

is defined by

a * b = \frac{2 a b}{5} .

2 * x = 3^{- 1}

then

x =

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Binary Operations

Define

a \otimes b = l c m (a, b) + g c d (a, b)

and

a \oplus b = a^{b} + b^{a}

. The value of

(1 \oplus 2) \otimes (3 \oplus 4)

is -

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

The number of binary operations on set

\{3 k / 1 \leq k \leq n; k, n \in N\}

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

Let

ℤ

be the set of all integers and let

*

be a binary operation

a * b = a + b + 10

for all

a, b \in ℤ

. The identity element of this group is

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

The identity element of the binary operation

*

R

defined by

a * b = \frac{a b}{4} \forall a, b \in R

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

*

is a binary operation such that

a * b = a^{2} + b^{2}

, then

3 * 5

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

The number of binary operations on the set

{1, 2, 3}

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

For the binary operation

*

defined on

R - \{1\}

by the rule

a * b = a + b + a b

for all

a, b \in R - \{1\}

, the inverse of

a

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Mathematics>Algebra>Set Theory and Relations>Binary Operations

In a group

G,

the equations

a x = b

and

y a = b

have

The binary operation * on Z+ defined by a*b=a-b is

Important Questions on Set Theory and Relations

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The binary operation $$ on $Z^{+}$ defined by $a b = a - b$ is