मराठी

Define a Reflexive Relation ?

Advertisements
Advertisements

प्रश्न

Define a reflexive relation ?

Advertisements

उत्तर

A relation R on A is said to be reflexive iff every element of A is related to itself.

i.e. R is reflexive  ⇔ (a, a) ∈ R for all a ∈ A

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations - Exercise 1.3 [पृष्ठ ३०]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 1 Relations
Exercise 1.3 | Q 10 | पृष्ठ ३०

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 of points in a plane given by R = {(P, Q) : distance of the point P from the origin is the same as the distance of the point Q from the origin} is an equivalence relation. Further, show that the set of all points related to a point P ≠ (0, 0) is the circle passing through P with the origin as its centre.


Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.


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


The following relation is defined on the set of real numbers.  aRb if |a| ≤ b

Find whether relation is reflexive, symmetric or transitive.


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


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


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 Z be the set of all integers and Z0 be the set of all non-zero integers. Let a relation R on Z × Z0be defined as (a, b) R (c, d) ⇔ ad = bc for all (a, b), (c, d) ∈ Z × Z0,
Prove that R is an equivalence relation on Z × Z0.


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 R = {(x, y) : |x2 − y2| <1) be a relation on set A = {1, 2, 3, 4, 5}. Write R as a set of ordered pairs.


Let R be the equivalence relation on the set Z of the integers given by R = { (a, b) : 2 divides a - b }.

Write the equivalence class [0].


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


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


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


Let R be the relation on the set A = {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then, _____________________ .


Let A = {1, 2, 3}. Then, the number of equivalence relations containing (1, 2) is ______.


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


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


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


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


If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is ______.


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


Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : |a2 – b2| < 8. Then R is given by ______.


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


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


Given set A = {1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be ____________.


An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions.

  • Ravi wishes to form all the relations possible from B to G. How many such relations are possible?

The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has nontrivial solution 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


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


A relation 'R' in a set 'A' is called a universal relation, if each element of' A' is related to :-


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 ______


Which relation is called an Empty Relation?


Which statement defines a Universal Relation?


Which relation is identified as an equivalence relation?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×