मराठी

Write the Domain of the Relation R Defined on the Set Z of Integers as Follows: (A, B) ∈ R ⇔ A2 + B2 = 25 - Mathematics

Advertisements
Advertisements

प्रश्न

Write the domain of the relation R defined on the set Z of integers as follows:-
(a, b) ∈ R ⇔ a2 + b2 = 25

बेरीज
Advertisements

उत्तर

Domain of R is the set of values satisfying the relation R.
As a should be an integer, we get the given values of a:-

0,  ±3 ±4,  ±5

Thus ,

Domain of {0, ±3, ±4, ±5}

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations - Exercise 1.3 [पृष्ठ २९]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 1 Relations
Exercise 1.3 | Q 1 | पृष्ठ २९

संबंधित प्रश्‍न

Let N denote the set of all natural numbers and R be the relation on N × N defined by (a, b) R (c, d) if ad (b + c) = bc (a + d). Show that R is an equivalence relation.


Given an example of a relation. Which is Symmetric and transitive but not reflexive.


Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is

(A) 1 (B) 2 (C) 3 (D) 4


Let A be the set of all human beings in a town at a particular time. Determine whether the following relation is reflexive, symmetric and transitive:

 R = {(x, y) : x and y work at the same place}


Three relations R1, R2 and R3 are defined on a set A = {a, b, c} as follows:
R1 = {(a, a), (a, b), (a, c), (b, b), (b, c), (c, a), (c, b), (c, c)}
R2 = {(a, a)}
R3 = {(b, c)}
R4 = {(a, b), (b, c), (c, a)}.

Find whether or not each of the relations R1, R2, R3, R4 on A is (i) reflexive (ii) symmetric and (iii) transitive.


If = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?


Let R be a relation defined on the set of natural numbers N as
R = {(xy) : x N, 2x + y = 41}
Find the domain and range of R. Also, verify whether R is (i) reflexive, (ii) symmetric (iii) transitive.


Show that the relation '≥' on the set R of all real numbers is reflexive and transitive but not symmetric ?


Defines a relation on N:

x + 4y = 10, x, y ∈ N

Determine the above relation is reflexive, symmetric and transitive.


Prove that the relation R on Z defined by
(a, b) ∈ R ⇔ a − b is divisible by 5
is an equivalence relation on Z.


Let R be the relation defined on the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.


If R and S are relations on a set A, then prove that R and S are symmetric ⇒ R ∩ S and R ∪ S are symmetric ?


Define an equivalence relation ?


R is a relation on the set Z of integers and it is given by
(x, y) ∈ R ⇔ | x − y | ≤ 1. Then, R is ______________ .


Let R be the relation over the set of all straight lines in a plane such that  l1 R l2 ⇔ l 1⊥ l2. Then, R is _____________ .


If A = {a, b, c}, then the relation R = {(b, c)} on A is _______________ .


Let A = {1, 2, 3}. Then, the number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is ______.


A relation ϕ from C to R is defined by x ϕ y ⇔ | x | = y. Which one is correct?


Let R be a relation on N defined by x + 2y = 8. The domain of R is _______________ .


Show that the relation R on R defined as R = {(a, b): a ≤ b}, is reflexive, and transitive but not symmetric.


Show that the relation S in the set A = [x ∈ Z : 0 ≤ x ≤ 12] given by S = [(a, b) : a, b ∈ Z, ∣a − b∣ is divisible by 3] is an equivalence relation.


If A = {a, b, c}, B = (x , y} find A × B.


If A = {a, b, c}, B = (x , y} find B × B.


Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6} Find (A × B) ∩ (A × C).


Let Z be the set of integers and R be the relation defined in Z such that aRb if a – b is divisible by 3. Then R partitions the set Z into ______ pairwise disjoint subsets


Consider the set A = {1, 2, 3} and the relation R = {(1, 2), (1, 3)}. R is a transitive relation.


If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, transitive but not symmetric


Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
a mapping from A to B which is not injective


Let us define a relation R in R as aRb if a ≥ b. Then R is ____________.


Let A = {1, 2, 3, …. n} and B = {a, b}. Then the number of surjections from A into B is ____________.


Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is ____________.


Total number of equivalence relations defined in the set S = {a, b, c} is ____________.


Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

  • Let R be a relation on B defined by R = {(1,2), (2,2), (1,3), (3,4), (3,1), (4,3), (5,5)}. Then R is:

In a group of 52 persons, 16 drink tea but not coffee, while 33 drink tea. How many persons drink coffee but not tea?


Let R1 and R2 be two relations defined as follows :

R1 = {(a, b) ∈ R2 : a2 + b2 ∈ Q} and

R2 = {(a, b) ∈ R2 : a2 + b2 ∉ Q}, where Q is the set of all rational numbers. Then ______


Let R = {(x, y) : x, y ∈ N and x2 – 4xy + 3y2 = 0}, where N is the set of all natural numbers. Then the relation R is ______.


Let A = {1, 2, 3, 4} and let R = {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is ______.


Let L be a set of all straight lines in a plane. The relation R on L defined as 'perpendicular to' is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×