English

Write the Identity Relation on Set a = {A, B, C}.

Advertisements
Advertisements

Question

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

One Line Answer
Sum
Advertisements

Solution

Identity set of A is

I = {(a, a), (b, b), (c, c)}

Every element of this relation is related to itself.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Relations - Exercise 1.3 [Page 30]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 1 Relations
Exercise 1.3 | Q 3 | Page 30

RELATED QUESTIONS

Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} 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 an equivalence relation. Find the set of all elements related to 1.


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


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.


Show that the relation R defined in the set A of all triangles as R = {(T1, T2) : T1 is similar to T2}, is an equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8, and 10. Which triangles among T1, T2 and T3 are related?


Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is ______.


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]


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.


Let A = {1, 2, 3}, and let R1 = {(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)}, R2 = {(2, 2), (3, 1), (1, 3)}, R3 = {(1, 3), (3, 3)}. Find whether or not each of the relations R1, R2, R3 on A is (i) reflexive (ii) symmetric (iii) transitive.


An integer m is said to be related to another integer n if m is a multiple of n. Check if the relation is symmetric, reflexive and transitive.


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.


Defines a relation on :
  x > y, x, y ∈  N

Determine the above relation is reflexive, symmetric and transitive.


Let n be a fixed positive integer. Define a relation R on Z as follows:
(a, b) ∈ R ⇔ a − b is divisible by n.
Show that R is an equivalence relation on Z.


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


Define a symmetric relation ?


State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive ?


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 R be a relation on the set N given by
R = {(a, b) : a = b − 2, b > 6}. Then,


In the set Z of all integers, which of the following relation R is not an equivalence relation ?


Show that the relation R defined by (a, b)R(c,d) ⇒ a + d = b + c   on the A x A  , where A =  {1, 2,3,...,10}  is an equivalence relation. Hence write the equivalence class [(3, 4)]; a, b, c,d ∈ A.


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) ∩ (A × C).


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

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


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


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


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 A = {1, 2, 3, ... 9} and R be the relation in A × A defined by (a, b) R(c, d) if a + d = b + c for (a, b), (c, d) in A × A. Prove that R is an equivalence relation and also obtain the equivalent class [(2, 5)]


Consider the 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 ______.


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


Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is ____________.


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?

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

  • Let R = `{ ("L"_1, "L"_2) ∶ "L"_1 bot "L"_2  "where"  "L"_1, "L"_2 in "L" }` which of the following is true?

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


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×