मराठी

Define a Commutative Binary Operation on a Set. - Mathematics

Advertisements
Advertisements

प्रश्न

Define a commutative binary operation on a set.

उत्तर

An operation * on a set A is called a commutative binary operation if and only if it is a binary operation as well as commutative, i.e. it must satisfy the following two conditions.

(i)abA,a,bA( Binary operation )
(ii)ab=ba,a,bA(Commutaive)

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Binary Operations - Exercise 3.6 [पृष्ठ ३५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 3 Binary Operations
Exercise 3.6 | Q 4 | पृष्ठ ३५

संबंधित प्रश्‍न

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 Z+, define * by a


For each binary operation * defined below, determine whether * is commutative or associative.

On Q, define ab + 1


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

on Q defined by ab=a1b+1for all a, bQ.


Let * be a binary operation on the set I of integers, defined by a * b = 2a + b − 3. Find the value of 3 * 4.


Find the total number of binary operations on {ab}.


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


 Check the commutativity and associativity of the following binary operation'*' on Q defined by a * b = ab + 1 for all a, b ∈ Q ?


If the binary operation o is defined by aob = a + b − ab on the set Q − {−1} of all rational numbers other than 1, shown that o is commutative on Q − [1].


On the set Z of integers a binary operation * is defined by a * b = ab + 1 for all a , b ∈ Z. Prove that * is not associative on Z.


If the binary operation * on the set Z is defined by a * b = a + b −5, the find the identity element with respect to *.


On R − {1}, a binary operation * is defined by a * b = a + b − ab. Prove that * is commutative and associative. Find the identity element for * on R − {1}. Also, prove that every element of R − {1} is invertible.


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 ?


Construct the composition table for ×6 on set S = {0, 1, 2, 3, 4, 5}.


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

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

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


Write the identity element for the binary operation * on the set R0 of all non-zero real numbers by the rule ab=ab2 for all ab ∈ R0.


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}.


Let * be a binary operation on N given by a * b = HCF (a, b), a, b ∈ N. Write the value of 22 * 4.


Mark the correct alternative in the following question:-

For the binary operation * on Z defined by a * b = a + b + 1, the identity element is ________________ .


If the binary operation ⊙ is defined on the set Q+ of all positive rational numbers by ab=ab4. Then ,3(1512) is equal to __________ .


The number of binary operation that can be defined on a set of 2 elements is _________ .


The number of commutative binary operations that can be defined on a set of 2 elements is ____________ .


Let A = ℝ × ℝ and let * be a binary operation on A defined by (a, b) * (c, d) = (ad + bc, bd) for all (a, b), (c, d) ∈ ℝ × ℝ.
(i) Show that * is commutative on A.
(ii) Show that * is associative on A.
(iii) Find the identity element of * in A.


If * is defined on the set R of all real numbers by *: a*b = a2+b2, find the identity elements, if it exists in R with respect to * .


Determine whether * is a binary operation on the sets-given below.

a * b – a.|b| on R


Fill in the following table so that the binary operation * on A = {a, b, c} is commutative.

* a b c
a b    
b c b a
c a   c

Let A = (101001011001), B = (010110101001), C = (110101101111) be any three boolean matrices of the same type. Find (A v B) ∧ C


Choose the correct alternative:

Subtraction is not a binary operation in


Choose the correct alternative:

Which one of the following is a binary operation on N?


Choose the correct alternative:

In the set Q define a ⨀ b = a + b + ab. For what value of y, 3 ⨀ (y ⨀ 5) = 7?


Choose the correct alternative:

If a * b = a2+b2 on the real numbers then * is


Is the binary operation * defined on Z (set of integer) by m * n = m – n + mn ∀ m, n ∈ Z commutative?


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

a * b = a – b for a, b ∈ Q


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

a * b = ab2 for a, b ∈ Q


Let N be the set of natural numbers. Then, the binary operation * in N defined as a * b = a + b, ∀ a, b ∈ N has identity element.


Let * be binary operation defined on R by a * b = 1 + ab, ∀ a, b ∈ R. Then the operation * is ______.


A binary operation on a set has always the identity element.


Let A = N x N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Then * is ____________.


Let * be a binary operation on the set of integers I, defined by a * b = a + b – 3, then find the value of 3 * 4.


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.