मराठी

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. - Mathematics

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प्रश्न

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.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

This statement is False.

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पाठ 1: Relations And Functions - Solved Examples [पृष्ठ ११]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 1 Relations And Functions
Solved Examples | Q 34 | पृष्ठ ११

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 a ∗ b = a – b


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

On Q, define ab + 1


Let * be a binary operation on the set of rational numbers as follows:

(i) − 

(ii) a2 + b2

(iii) ab 

(iv) = (− b)2

(v) a * b = ab/4

(vi) ab2

Find which of the binary operations are commutative and which are associative.


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

On Z+, defined * by a * b = ab

Here, Z+ denotes the set of all non-negative integers.


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

On Z+ define * by a * b = |a − b|

Here, Z+ denotes the set of all non-negative integers.


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


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 ?


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


On the set Q of all ration numbers if a binary operation * is defined by \[a * b = \frac{ab}{5}\] , prove that * is associative on Q.


On Q, the set of all rational numbers a binary operation * is defined by \[a * b = \frac{a + b}{2}\] Show that * is not associative on Q.


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

Show that 'o' is both commutative and associate ?


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

Show that '*' is both commutative and associative on A ?


Let * be the binary operation on N defined by a * b = HCF of a and b.
Does there exist identity for this binary operation one N ?


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


Define an associative binary operation on a set.


Let * be a binary operation, on the set of all non-zero real numbers, given by \[a * b = \frac{ab}{5} \text { for all a, b } \in R - \left\{ 0 \right\}\]

Write the value of x given by 2 * (x * 5) = 10.


If the binary operation * on the set Z of integers is defined by a * b = a + 3b2, find the value of 2 * 4.


If a * b = a2 + b2, then the value of (4 * 5) * 3 is _____________ .


If G is the set of all matrices of the form

\[\begin{bmatrix}x & x \\ x & x\end{bmatrix}, \text{where x } \in R - \left\{ 0 \right\}\] then the identity element with respect to the multiplication of matrices as binary operation, is ______________ .


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


Subtraction of integers is ___________________ .


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


Let A = `((1, 0, 1, 0),(0, 1, 0, 1),(1, 0, 0, 1))`, B = `((0, 1, 0, 1),(1, 0, 1, 0),(1, 0, 0, 1))`, C = `((1, 1, 0, 1),(0, 1, 1, 0),(1, 1, 1, 1))` be any three boolean matrices of the same type. Find (A ∧ B) v C


Choose the correct alternative:

A binary operation on a set S is a function from


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

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


Let * be a binary operation on set Q of rational numbers defined as a * b `= "ab"/5`. Write the identity for * ____________.


a * b = `((a + b))/2` ∀a, b ∈ N is


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