English

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

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

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

Let g: A → B denote a mapping such that g = {(2, 2), (3, 2), (4, 5)}, which is not 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 Exemplar [English] Class 12
Chapter 1 Relations And Functions
Exercise | Q 18. (b) | Page 12

RELATED QUESTIONS

Show that the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1.


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


Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choose the correct answer.


The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*4


Test whether the following relation R2 is (i) reflexive (ii) symmetric and (iii) transitive:

R2 on Z defined by (a, b) ∈ R2 ⇔ |a – b| ≤ 5


Test whether the following relation R3 is (i) reflexive (ii) symmetric and (iii) transitive:

R3 on R is defined by (a, b) ∈ R3 `⇔` a2 – 4ab + 3b2 = 0.


The following relation is defined on the set of real numbers.
aRb if a – b > 0

Find whether relation is reflexive, symmetric or transitive.


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


Defines a relation on N:

x + 4y = 10, x, y ∈ N

Determine the above relation is reflexive, symmetric and transitive.


Show that the relation R, defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have the same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right-angled triangle T with sides 3, 4 and 5?


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 ?


If R = {(x, y) : x2 + y2 ≤ 4; x, y ∈ Z} is a relation on Z, write the domain of R.


Write the smallest reflexive relation on set A = {1, 2, 3, 4}.


If R = {(x, y) : x + 2y = 8} is a relation on N by, then write the range of R.


Define a reflexive relation ?


For the set A = {1, 2, 3}, define a relation R on the set A as follows:
R = {(1, 1), (2, 2), (3, 3), (1, 3)}
Write the ordered pairs to be added to R to make the smallest equivalence relation.


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 ______.


The relation 'R' in N × N such that
(a, b) R (c, d) ⇔ a + d = b + c is ______________ .


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


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


For the matrix A = `[(2,3),(5,7)]`, find (A + A') and verify that it is a symmetric matrix.


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


Let n be a fixed positive integer. Define a relation R in Z as follows: ∀ a, b ∈ Z, aRb if and only if a – b is divisible by n. Show that R is an equivalance relation


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


The following defines a relation on N:
x + y = 10, x, y ∈ N
Determine which of the above relations are 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 R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.


An integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.


Which of the following is not an equivalence relation on I, the set of integers: x, y


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


Let A = {1, 2, 3}, then the domain of the relation R = {(1, 1), (2, 3), (2, 1)} defined on A is ____________.


Let R be the relation “is congruent to” on the set of all triangles in a plane is ____________.


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


Given triangles with sides T1: 3, 4, 5; T2: 5, 12, 13; T3: 6, 8, 10; T4: 4, 7, 9 and a relation R inset of triangles defined as R = `{(Delta_1, Delta_2) : Delta_1  "is similar to"  Delta_2}`. Which triangles belong to the same equivalence class?


A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever


Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}

  • Mr. Shyam exercised his voting right in General Election-2019, then Mr. Shyam is related to which of the following?

If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘x is smaller than y’. The range of R is ____________.


If A is a finite set consisting of n elements, then the number of reflexive relations on A is


A relation in a set 'A' is known as empty relation:-


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×