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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.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

This statement is False.

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

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

संबंधित प्रश्न

Let * be a binary operation, on the set of all non-zero real numbers, given by `a** b = (ab)/5` for all a,b∈ R-{0} that 2*(x*5)=10


Let A = Q ✕ Q, where Q is the set of all rational numbers, and * be a binary operation defined on A by (a, b) * (c, d) =  (ac, b + ad), for all (a, b) (c, d) ∈ A.
Find
(i) the identity element in A
(ii) the invertible element of A.

(iii)and hence write the inverse of elements (5, 3) and (1/2,4)


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


State whether the following statements are true or false. Justify.

For an arbitrary binary operation * on a set N= ∀  N.


Determine whether the following operation define a binary operation on the given set or not : '*' on N defined by a * b = a + b - 2 for all a, b ∈ N


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 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

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 R, define * by a * b = a + 4b2

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


Is * defined on the set {1, 2, 3, 4, 5} by a * b = LCM of a and b a binary operation? Justify your answer.


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


Determine which of the following binary operations are associative and which are commutative : * on Q defined by \[a * b = \frac{a + b}{2} \text{ for all a, b } \in Q\] ?


Check the commutativity and associativity of the following binary operations '*'. on N defined by a * b = 2ab for all a, b ∈ N ?


Check the commutativity and associativity of the following binary operation  '*' on R defined by a * b = a + b − 7 for all ab ∈ R ?


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


Find the inverse of 5 under multiplication modulo 11 on Z11.


On the set Z of all integers a binary operation * is defined by a * b = a + b + 2 for all ab ∈ Z. Write the inverse of 4.


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.


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


If the binary operation * on Z is defined by a * b = a2 − b2 + ab + 4, then value of (2 * 3) * 4 is ____________ .


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 ________________ .


Let * be a binary operation on R defined by a * b = ab + 1. Then, * is _________________ .


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

a * b – a.|b| on R


Define an operation * on Q as follows: a * b = `(("a" + "b")/2)`; a, b ∈ Q. Examine the closure, commutative and associate properties satisfied by * on Q.


Let A be Q\{1} Define * on A by x * y = x + y – xy. Is * binary on A? If so, examine the commutative and associative properties satisfied by * on A


Choose the correct alternative:

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


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


A binary operation A × A → is said to be associative if:-


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