हिंदी

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.

Advertisements
Advertisements

प्रश्न

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.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Exercise [पृष्ठ १७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 1 Relations And Functions
Exercise | Q 53 | पृष्ठ १७

संबंधित प्रश्न

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.


Show that the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by R = {(a, b) : |a – b| is a multiple of 4} is an equivalence relation. Find the set of all elements related to 1.


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


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 = {x ∈ Z : 0 ≤ x ≤ 12}. Show that R = {(ab) : a∈ A, |a – b| is divisible by 4}is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]


The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*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 live in the same locality}


Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.


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


Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, add a minimum number of ordered pairs so that the enlarged relation is symmeteric, transitive and reflexive.


Let A = {1, 2, 3} and R = {(1, 2), (1, 1), (2, 3)} be a relation on A. What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A.


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


m is said to be related to n if m and n are integers and m − n is divisible by 13. Does this define 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 smallest reflexive relation on set A = {1, 2, 3, 4}.


Let the relation R be defined on N by aRb iff 2a + 3b = 30. Then write R as a set of ordered pairs


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


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


Let A = {2, 3, 4, 5, ..., 17, 18}. Let '≃' be the equivalence relation on A × A, cartesian product of Awith itself, defined by (a, b) ≃ (c, d) if ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is _______________ .


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


Mark the correct alternative in the following question:

The relation S defined on the set R of all real number by the rule aSb if a  b 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 T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b for all a, b  T. Then, R is ____________ .


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


Write the relation in the Roster form and hence find its domain and range :
R1 = {(a, a2) / a is prime number less than 15}


R = {(a, b) / b = a + 1, a ∈ Z, 0 < a < 5}. Find the Range of R.


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


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


Give an example of a map which is not one-one but onto


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 us define a relation R in R as aRb if a ≥ b. 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 ∶ B → B be defined by R = {(x, y): y is divisible by x} 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:

The relation R = {(1,1),(2,2),(3,3)} on {1,2,3} is ____________.


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


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


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 N be the set of all natural numbers and R be a relation on N × N defined by (a, b) R (c, d) `⇔` ad = bc for all (a, b), (c, d) ∈ N × N. Show that R is an equivalence relation on N × N. Also, find the equivalence class of (2, 6), i.e., [(2, 6)].


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×