English

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. - Mathematics

Advertisements
Advertisements

Question

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.

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is False.

Explanation:

Given that, R = {(3, 1), (1, 3), (3, 3)} be defined on the set A = {1, 2, 

Since (1, 1) ∉ R, R is not reflexive.

Since (3, 1) ∈ R ⇒ (1, 3) ∈ R, R is symmetric.

Since, (1, 3) ∈ R, (3, 1) ∈ R

But (1, 1) ∉ R

Hence, R is not transitive.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Relations And Functions - Exercise [Page 17]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 1 Relations And Functions
Exercise | Q 53 | Page 17

RELATED QUESTIONS

If R=[(x, y) : x+2y=8] is a relation on N, write the range of R.


Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have the same number of pages} is an equivalence relation.


Given an example of a relation. Which is Transitive but neither reflexive nor symmetric.


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


Given a non-empty set X, consider P(X), which is the set of all subsets of X. Define the relation R in P(X) as follows:

For subsets A, B in P(X), ARB if and only if A ⊂ B. Is R an equivalence relation on P(X)? Justify your answer.


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}


The following relation is defined on the set of real numbers.

aRb if 1 + ab > 0

Find whether relation is reflexive, symmetric or transitive.


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


Give an example of a relation which is symmetric and transitive but not reflexive?


Let A = {abc} and the relation R be defined on A as follows: R = {(aa), (bc), (ab)}. Then, write minimum number of ordered pairs to be added in R to make it reflexive and transitive.


Show that the relation R on the set Z of integers, given by
R = {(a, b) : 2 divides a – b},  is an equivalence relation.


Let C be the set of all complex numbers and Cbe the set of all no-zero complex numbers. Let a relation R on Cbe defined as

`z_1 R  z_2  ⇔ (z_1 -z_2)/(z_1 + z_2)` is real for all z1, z2 ∈ C0.

Show that R is an equivalence relation.


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


Write the identity relation on set A = {a, b, c}.


Let R = {(a, a3) : a is a prime number less than 5} be a relation. Find the range of R.


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


If R is the largest equivalence relation on a set A and S is any relation on A, then _____________ .


If R is a relation on the set A = {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3)}, then R is ____________ .


Mark the correct alternative in the following question:

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 _______________ .


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 ______________ .


Write the relation in the Roster form and hence find its domain and range:

R2 = `{("a", 1/"a")  "/"  0 < "a" ≤ 5, "a" ∈ "N"}`


For real numbers x and y, define xRy if and only if x – y + `sqrt(2)` is an irrational number. Then the relation R is ______.


Give an example of a map which is neither one-one nor onto


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.


Let A = { 2, 3, 6 } Which of the following relations on A are reflexive?


If A is a finite set containing n distinct elements, then the number of relations on A is equal to ____________.


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


A relation R on a non – empty set A is an equivalence relation if it is ____________.


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 S = {1, 2, 3, 4, 5} and let A = S x S. Define the relation R on A as follows:
(a, b) R (c, d) iff ad = cb. Then, R is ____________.


Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is ____________.


The relation > (greater than) on the set of real numbers is


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


On the set N of all natural numbers, define the relation R by a R b, if GCD of a and b is 2. Then, R is


The number of surjective functions from A to B where A = {1, 2, 3, 4} and B = {a, b} is


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


If f(x + 2a) = f(x – 2a), then f(x) is:


Define the relation R in the set N × N as follows:

For (a, b), (c, d) ∈ N × N, (a, b) R (c, d) if ad = bc. Prove that R is an equivalence relation in N × N.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×