Advertisements
Advertisements
प्रश्न
Write the smallest equivalence relation on the set A = {1, 2, 3} ?
उत्तर
The smallest equivalence relation on the set A = {1, 2, 3} is R = {(1, 1), (2, 2), (3, 3)}
APPEARS IN
संबंधित प्रश्न
determination of whether the following relations are reflexive, symmetric, and transitive:
Relation R in the set A = {1, 2, 3...13, 14} defined as R = {(x,y):3x - y = 0}
Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b) : |a - b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.
Given an example of a relation. Which is Reflexive and symmetric but not transitive.
Given an example of a relation. Which is Reflexive and transitive but not symmetric.
Three relations R1, R2 and R3 are defined on a set A = {a, b, c} as follows:
R1 = {(a, a), (a, b), (a, c), (b, b), (b, c), (c, a), (c, b), (c, c)}
R2 = {(a, a)}
R3 = {(b, c)}
R4 = {(a, b), (b, c), (c, a)}.
Find whether or not each of the relations R1, R2, R3, R4 on A is (i) reflexive (ii) symmetric and (iii) transitive.
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.
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?
If A = {1, 2, 3, 4} define relations on A which have properties of being symmetric but neither reflexive nor transitive ?
Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.
Give an example of a relation which is reflexive and transitive but not symmetric ?
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.
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 on the set Z of integers, given by
R = {(a, b) : 2 divides a – b}, is an equivalence relation.
If R and S are relations on a set A, then prove that R is reflexive and S is any relation ⇒ R ∪ S is reflexive ?
Define a symmetric relation ?
Define a transitive relation ?
If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.
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' in N × N such that
(a, b) R (c, d) ⇔ a + d = b + c is ______________ .
R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x − 3. Then, R−1 is ______________ .
Let A = {1, 2, 3} and B = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ________________ .
If R is the largest equivalence relation on a set A and S is any relation on A, then _____________ .
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 ______________ .
If A = {a, b, c}, B = (x , y} find A × A.
Write the relation in the Roster form and hence find its domain and range:
R2 = `{("a", 1/"a") "/" 0 < "a" ≤ 5, "a" ∈ "N"}`
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, transitive but not symmetric
Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
an injective mapping from A to B
Let A = { 2, 3, 6 } Which of the following relations on A are reflexive?
Let A = {1, 2, 3, 4, 5, 6} Which of the following partitions of A correspond to an equivalence relation on A?
If f(x) = `1 - 1/"x", "then f"("f"(1/"x"))` ____________.
The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R-1 is given by ____________.
A relation R in set A = {1, 2, 3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A?
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 relation R be defined by R = {(L1, L2): L1║L2 where L1, L2 ∈ L} then R is ____________ relation.
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
The number of surjective functions from A to B where A = {1, 2, 3, 4} and B = {a, b} is
There are 600 student in a school. If 400 of them can speak Telugu, 300 can speak Hindi, then the number of students who can speak both Telugu and Hindi is:
A relation in a set 'A' is known as empty relation:-