मराठी

Let R be the set of real numbers and * be the binary operation defined on R as a * b = a + b – ab ∀ a, b ∈ R. Then, the identity element with respect to the binary operation * is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

Let R be the set of real numbers and * be the binary operation defined on R as a * b = a + b – ab ∀ a, b ∈ R. Then, the identity element with respect to the binary operation * is ______.

रिकाम्या जागा भरा

उत्तर

Let R be the set of real numbers and * be the binary operation defined on R as a * b = a + b – ab ∀ a, b ∈ R. Then, the identity element with respect to the binary operation * is 0 is the identity element with respect to the binary operation *.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations And Functions - Solved Examples [पृष्ठ १०]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 1 Relations And Functions
Solved Examples | Q 29 | पृष्ठ १०

संबंधित प्रश्‍न

Determine whether or not of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this.

On Z+, define * by ab


Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this.

On R, define * by ab2


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

(i) Compute (2 * 3) * 4 and 2 * (3 * 4)

(ii) Is * commutative?

(iii) Compute (2 * 3) * (4 * 5).

(Hint: use the following 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

Find which of the operations given above has identity.


Determine whether the following operation define a binary operation on the given set or not :

\[' +_6 ' \text{on S} = \left\{ 0, 1, 2, 3, 4, 5 \right\} \text{defined by}\] 
\[a +_6 b = \begin{cases}a + b & ,\text{ if a} + b < 6 \\ a + b - 6 & , \text{if a} + b \geq 6\end{cases}\]


Determine whether the following operation define a binary operation on the given set or not :

\[' * ' \text{on Q defined by } a * b = \frac{a - 1}{b + 1} \text{for all a, b} \in Q .\]


Let S be the set of all rational numbers of the form \[\frac{m}{n}\] , where m ∈ Z and n = 1, 2, 3. Prove that * on S defined by a * b = ab is not a binary operation.


Let '*' be a binary operation on N defined by a * b = 1.c.m. (a, b) for all a, b ∈ N

Check the commutativity and associativity of '*' on N.


Determine which of the following binary operation is associative and which is commutative : * on N defined by a * b = 1 for all a, b ∈ N ?


Check the commutativity and associativity of the following binary operation 'o' on Q defined by \[\text{a o b }= \frac{ab}{2}\] for all a, b ∈ Q ?


Check the commutativity and associativity of the following binary operation '*' on Q defined by a * b = ab2 for all ab ∈ Q ?


Check the commutativity and associativity of the following binary operation '*' on N, defined by a * b = ab for all ab ∈ N ?


On Q, the set of all rational numbers, * is defined by \[a * b = \frac{a - b}{2}\] , shown that * is no associative ?


Let S be the set of all rational numbers except 1 and * be defined on S by a * b = a + b \[-\] ab, for all a, b \[\in\] S:

Prove that * is a binary operation on S ?


Find the identity element in the set of all rational numbers except −1 with respect to *defined by a * b = a + b + ab.


Let * be a binary operation on Z defined by
a * b = a + b − 4 for all a, b ∈ Z Find the identity element in Z ?


Let 'o' be a binary operation on the set Q0 of all non-zero rational numbers defined by \[a o b = \frac{ab}{2}, \text{ for all a, b } \in Q_0\] :

 Find the identity element in Q0.


Let R0 denote the set of all non-zero real numbers and let A = R0 × R0. If '*' is a binary operation on A defined by

(a, b) * (c, d) = (ac, bd) for all (a, b), (c, d) ∈ A

Find the invertible element in A ?


Define a binary operation on a set.


Write the composition table for the binary operation multiplication modulo 10 (×10) on the set S = {2, 4, 6, 8}.


A binary operation * is defined on the set R of all real numbers by the rule \[a * b = \sqrt{  a^2 + b^2} \text{for all a, b } \in R .\]

Write the identity element for * on R.


The binary operation * defined on N by a * b = a + b + ab for all a, b N is ________________ .


The binary operation * is defined by a * b = a2 + b2 + ab + 1, then (2 * 3) * 2 is equal to ______________ .


Let * be a binary operation on Q+ defined by \[a * b = \frac{ab}{100} \text{ for all a, b } \in Q^+\] The inverse of 0.1 is _________________ .


Consider the binary operation * defined by the following tables on set S = {a, bcd}.

a b c  d
a a b c d
b b a d c
c c d a b
d d c b a


Show that the binary operation is commutative and associative. Write down the identities and list the inverse of elements.


Choose the correct alternative:

In the set R of real numbers ‘*’ is defined as follows. Which one of the following is not a binary operation on R?


Choose the correct alternative:

If a * b = `sqrt("a"^2 + "b"^2)` on the real numbers then * is


Let * be the binary operation defined on Q. Find which of the following binary operations are commutative

a * b = a2 + b2 ∀ a, b ∈ Q


Let * be a binary operation on set Q – {1} defind by a * b = a + b – ab : a, b ∈ Q – {1}. Then * is ____________.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.