English

Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:an injective mapping from A to B - Mathematics

Advertisements
Advertisements

Question

Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
an injective mapping from A to B

Sum

Solution

Given, A = {2, 3, 4}, B = {2, 5, 6, 7}

Let f: A → B denote a mapping

f = {(x, y): y = x + 3}

or

f = {(2, 5), (3, 6), (4, 7)}, which is an injective mapping.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Relations And Functions - Exercise [Page 12]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 1 Relations And Functions
Exercise | Q 18. (a) | Page 12

RELATED QUESTIONS

Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.


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


Give an example of a relation which is symmetric but neither reflexive nor transitive?


Let Z be the set of integers. Show that the relation
 R = {(a, b) : a, b ∈ Z and a + b is even}
is an equivalence relation on Z.


Let S be a relation on the set R of all real numbers defined by
S = {(a, b) ∈ R × R : a2 + b2 = 1}
Prove that S is not an equivalence relation on R.


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 a symmetric relation ?


Let A = {2, 3, 4, 5} and B = {1, 3, 4}. If R is the relation from A to B given by a R b if "a is a divisor of b". Write R as a set of ordered pairs.


If a relation R is defined on the set Z of integers as follows:
(a, b) ∈ R ⇔ a2 + b2 = 25. Then, domain (R) is ___________


The relation R defined on the set A = {1, 2, 3, 4, 5} by
R = {(a, b) : | a2 − b2 | < 16} is given by ______________ .


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 ______.


S is a relation over the set R of all real numbers and it is given by (a, b) ∈ S ⇔ ab ≥ 0. Then, S is _______________ .


Mark the correct alternative in the following question:

Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then, R is _____________ .


Mark the correct alternative in the following question:

Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m  L. Then, R is ______________ .


Mark the correct alternative in the following question:

Consider a non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then, R is _____________ .


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


Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if and only if l is perpendicular to m ∀ l, m ∈ L. Then R is ______.


If A = {1, 2, 3, 4 }, define relations on A which have properties of being: 
symmetric but neither reflexive nor transitive


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


The following defines a relation on N:
x y is square of an integer x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.


Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. Then R is ______.


Let the relation R be defined in N by aRb if 2a + 3b = 30. Then R = ______.


R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A, then R is ____________.


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


The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R-1 is given by ____________.


Given set A = {a, b, c}. An identity relation in set A is ____________.


Which one of the following relations on the set of real numbers R is an equivalence relation?


There are 600 student in a school. If 400 of them can speak Telugu, 300 can speak Hindi, then the number of students who can speak both Telugu and Hindi is:


Which of the following is/are example of symmetric


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×