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

Advertisements
Advertisements

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
Advertisements

उत्तर

This statement is False.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations And Functions - Solved Examples [पृष्ठ ११]

APPEARS IN

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 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


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 = |− b|


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

On Z, define − b


Let * be the binary operation on given by a * = L.C.M. of and b. Find

(i) 5 * 7, 20 * 16

(ii) Is * commutative?

(iii) Is * associative?

(iv) Find the identity of * in N

(v) Which elements of are invertible for the operation *?


Given a non-empty set X, consider the binary operation *: P(X) × P(X) → P(X) given by A * B = A ∩ B &mnForE; AB in P(X) is the power set of X. Show that is the identity element for this operation and is the only invertible element in P(X) with respect to the operation*.


Define a binary operation *on the set {0, 1, 2, 3, 4, 5} as

a * b = `{(a+b, "if a+b < 6"), (a + b - 6, if a +b >= 6):}`

Show that zero is the identity for this operation and each element a ≠ 0 of the set is invertible with 6 − a being the inverse of a.


Discuss the commutativity and associativity of binary operation '*' defined on A = Q − {1} by the rule a * ba − b + ab for all, a, b ∊ A. Also find the identity element of * in A and hence find the invertible elements of A.


If a * b denotes the larger of 'a' and 'b' and if a∘b = (a * b) + 3, then write the value of (5) ∘ (10), where * and ∘ are binary operations.


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.


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


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 ?


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 Q defined by a * b = a − b for all a, b ∈ Q ?


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.


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


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 ?


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


For the binary operation ×10 on set S = {1, 3, 7, 9}, find the inverse of 3.


Write the multiplication table for the set of integers modulo 5.


For the binary operation multiplication modulo 10 (×10) defined on the set S = {1, 3, 7, 9}, write the inverse of 3.


If a * b denote the bigger among a and b and if a ⋅ b = (a * b) + 3, then 4.7 = __________ .


If a binary operation * is defined on the set Z of integers as a * b = 3a − b, then the value of (2 * 3) * 4 is ___________ .


An operation * is defined on the set Z of non-zero integers by \[a * b = \frac{a}{b}\]  for all ab ∈ Z. Then the property satisfied is _______________ .


On Z an operation * is defined by a * b = a2 + b2 for all a, b ∈ Z. The operation * on Z is _______________ .


On the set Q+ of all positive rational numbers a binary operation * is defined by \[a * b = \frac{ab}{2} \text{ for all, a, b }\in Q^+\]. The inverse of 8 is _________ .


The number of binary operation 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 number by *: a * b = `sqrt(a^2 + b^2)` find the identity element if exist in R with respect to *


Let M = `{{:((x, x),(x, x)) : x ∈ "R"- {0}:}}` and let * be the matrix multiplication. Determine whether M is closed under *. If so, examine the commutative and associative properties satisfied by * on M


Choose the correct alternative:

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


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 set Q – {1} defind by a * b = a + b – ab : a, b ∈ Q – {1}. 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.


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


Determine which of the following binary operation on the Set N are associate and commutaive both.


Subtraction and division are not binary operation on.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×