Class 12 Exam > Class 12 Videos > L38 : Binary Operations Identity - Relations and Functions, Maths, Class 12
L38 : Binary Operations Identity - Relations and Functions, Maths, Class 12 Video Lecture
FAQs on L38 : Binary Operations Identity - Relations and Functions, Maths, Class 12 Video Lecture
| 1. What is the identity element for binary operations? |  |
Ans. The identity element for binary operations is an element that, when combined with any other element through the binary operation, leaves the other element unchanged. In other words, if 'a' is an element and 'e' is the identity element, then the binary operation (a * e) or (e * a) results in 'a' itself.
| 2. How are binary operations related to relations and functions? | |
Ans. Binary operations are related to relations and functions in the sense that they can be used to define and analyze these mathematical concepts. Binary operations help establish relationships between elements in a set and can be used to define functions in terms of inputs and outputs.
| 3. Can a binary operation have more than one identity element? | |
Ans. No, a binary operation can have at most one identity element. If there were multiple identity elements, it would lead to ambiguity and would violate the properties of binary operations. Therefore, by definition, a binary operation can have only one identity element.
| 4. Are all binary operations commutative? | |
Ans. No, not all binary operations are commutative. A binary operation is said to be commutative if changing the order of the operands does not affect the result. For example, addition is a commutative operation as a + b = b + a. However, subtraction and division are not commutative as a - b ≠ b - a and a ÷ b ≠ b ÷ a.
| 5. How are binary operations different from unary operations? | |
Ans. Binary operations involve two operands or elements on which the operations are performed, resulting in a single output. On the other hand, unary operations involve a single operand or element and produce a single output. In simple terms, binary operations require two inputs, while unary operations require only one input.
Text Transcript from Video
hello friends this video on relation and
functions part 38 is brought you by exam
fear calm no more fear from exam before
watching this video please make sure
that you have watched part more departed
let's understand identity binary
operation what is identity might not if
there exists element E that is part of
obviously set a because we're talking
about the operation on set a only says
that any number in to e into not any
number operation E is equal to a and
that is equal to e operation if such e
exist then it is an identity finally
operation will take some example so you
have to show that zero is the identity
operation or addition on and one is the
identity for multiplication on so if you
see you take any number you add that
number with zero this becomes a Louie
and it is also equal to all pursue thus
we can say that zero is a identity
addition operation on I say for one you
take any number we multiply with 1 you
get R or you multiply this way so as you
can see that 1 is the identity
multiplication operation now there is no
iron Indian 4 - 4 - if you see I don't
have any number actually what our little
any number you subtract with E in R or
Imai nasai this there is no such number
actually even if you take 0 this becomes
R this becomes minus R so actually there
is no such number no such number exists
which satisfies it
so I can say that there is no identity
operation 1 - similarly for division
also when I say a divided e equal to eg
by a and this should be equal to a for
identity operation to exist but we know
that there is no such number exist no
such a exist that satisfy this condition
in a family as one this becomes ml 1
this becomes 1 by 8 and they are not
same please note 0 is the identity for
addition operation on ha but it is non
identity for addition operation on then
why because 0 is not national number
please note because if you are taking
any value then and we are saying that
that number is the identity operator
operation or that number is the identity
then that number has to be part of the
set example from telling 0 is the
identity for addition operation on our
that means 0 with the member of our and
I'd say 0 is a identity operation on n
then 0 I ask you paper of natural number
but that is not the case so 0 cannot be
the identity operation on nationalism 0
is a identity for addition operation on
real number and there is no addition
operation there is no identity for
addition operation it does not existence
thank you visit exam viacom to watch
free education videos try free online
deaths get the best quality study
materials study from the best tutors and
mentors and much more
thanks and screen
functions part 38 is brought you by exam
fear calm no more fear from exam before
watching this video please make sure
that you have watched part more departed
let's understand identity binary
operation what is identity might not if
there exists element E that is part of
obviously set a because we're talking
about the operation on set a only says
that any number in to e into not any
number operation E is equal to a and
that is equal to e operation if such e
exist then it is an identity finally
operation will take some example so you
have to show that zero is the identity
operation or addition on and one is the
identity for multiplication on so if you
see you take any number you add that
number with zero this becomes a Louie
and it is also equal to all pursue thus
we can say that zero is a identity
addition operation on I say for one you
take any number we multiply with 1 you
get R or you multiply this way so as you
can see that 1 is the identity
multiplication operation now there is no
iron Indian 4 - 4 - if you see I don't
have any number actually what our little
any number you subtract with E in R or
Imai nasai this there is no such number
actually even if you take 0 this becomes
R this becomes minus R so actually there
is no such number no such number exists
which satisfies it
so I can say that there is no identity
operation 1 - similarly for division
also when I say a divided e equal to eg
by a and this should be equal to a for
identity operation to exist but we know
that there is no such number exist no
such a exist that satisfy this condition
in a family as one this becomes ml 1
this becomes 1 by 8 and they are not
same please note 0 is the identity for
addition operation on ha but it is non
identity for addition operation on then
why because 0 is not national number
please note because if you are taking
any value then and we are saying that
that number is the identity operator
operation or that number is the identity
then that number has to be part of the
set example from telling 0 is the
identity for addition operation on our
that means 0 with the member of our and
I'd say 0 is a identity operation on n
then 0 I ask you paper of natural number
but that is not the case so 0 cannot be
the identity operation on nationalism 0
is a identity for addition operation on
real number and there is no addition
operation there is no identity for
addition operation it does not existence
thank you visit exam viacom to watch
free education videos try free online
deaths get the best quality study
materials study from the best tutors and
mentors and much more
thanks and screen
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