MATHEMATICS PART I Textbook for Class XII>Chapter 1 - Relations and Functions>EXERCISE 1.4>Q 4

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Consider a binary operation $$ on the set $\{1, 2, 3, 4, 5\}$ given by the following multiplication table. Compute $(2 3) * (4 * 5) .$

* 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

Important Questions on Relations and Functions

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MATHEMATICS PART I Textbook for Class XII>Chapter 1 - Relations and Functions>EXERCISE 1.4>Q 5

The binary operation

*

on the set

\{1, 2, 3, 4, 5\}

is given by the following multiplication table.

$*$	$1$	$2$	$3$	$4$	$5$
$1$	$1$	$1$	$1$	$1$	$1$
$2$	$1$	$2$	$1$	$2$	$1$
$3$	$1$	$1$	$3$	$1$	$1$
$4$	$1$	$2$	$1$	$4$	$1$
$5$	$1$	$1$	$1$	$1$	$5$

Let

*^{'}

be the binary operation on the set

\{1, 2, 3, 4, 5\}

defined by

a *^{'} b = H . C . F

. of

a

and

b

. Is the operation

*^{'}

same as the operation

*

defined above? Justify your answer.

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MATHEMATICS PART I Textbook for Class XII>Chapter 1 - Relations and Functions>EXERCISE 1.4>Q 6

Let

*

be the binary operation on

N

given by

a * b = L . C . M

. of

a

and

b

. Find

5 * 7, 20 * 16 .

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MATHEMATICS PART I Textbook for Class XII>Chapter 1 - Relations and Functions>EXERCISE 1.4>Q 6

Let

*

be the binary operation on

N

given by

a * b = L . C . M .

of

a

and

b

.
Is

*

commutative?

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IMPORTANT

MATHEMATICS PART I Textbook for Class XII>Chapter 1 - Relations and Functions>EXERCISE 1.4>Q 6

Let

*

be the binary operation on

N

given by

a * b = L . C . M

. of

a

and

b

.
Is

*

associative?

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IMPORTANT

MATHEMATICS PART I Textbook for Class XII>Chapter 1 - Relations and Functions>EXERCISE 1.4>Q 6

Let

*

be the binary operation on

N

given by

a * b

= L.C.M. of

a

and

b

.

Find the identity of

*

in

N .

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IMPORTANT

MATHEMATICS PART I Textbook for Class XII>Chapter 1 - Relations and Functions>EXERCISE 1.4>Q 6

Let

*

be the binary operation on

N

a * b

=

L.C.M. of

a

and

b

. Which elements of

N

are invertible for the operation

*

?

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MATHEMATICS PART I Textbook for Class XII>Chapter 1 - Relations and Functions>EXERCISE 1.4>Q 7

Is

*

defined on the set

\{1, 2, 3, 4, 5\}

by

a * b = L . C . M

. of

a

and

b

a binary operation? Justify your answer.

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IMPORTANT

MATHEMATICS PART I Textbook for Class XII>Chapter 1 - Relations and Functions>EXERCISE 1.4>Q 8

Let

*

be the binary operation on

N

defined by

a * b = H . C . F .

of

a

and

b .

Is

*

commutative? Is

*

associative? Does there exist identity for this binary operation on

N

?