Advertisements
Advertisements
प्रश्न
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 ______.
पर्याय
Reflexive
Symmetric
Transitive
None of these
Advertisements
उत्तर
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 reflexive.
APPEARS IN
संबंधित प्रश्न
Given an example of a relation. Which is symmetric but neither reflexive nor transitive.
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 = {x ∈ Z : 0 ≤ x ≤ 12}. Show that R = {(a, b) : a, b ∈ 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]
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 is wife of y}
The following relation is defined on the set of real numbers.
aRb if a – b > 0
Find whether relation is reflexive, symmetric or transitive.
Give an example of a relation which is transitive but neither reflexive nor symmetric?
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 defined by R = {(a, b) : a – b is divisible by 3; a, b ∈ Z} is an equivalence relation.
If R and S are transitive relations on a set A, then prove that R ∪ S may not be a transitive relation on A.
Write the identity relation on set A = {a, b, c}.
Write the smallest reflexive relation on set A = {1, 2, 3, 4}.
State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive ?
R is a relation on the set Z of integers and it is given by
(x, y) ∈ R ⇔ | x − y | ≤ 1. Then, R is ______________ .
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 = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is _______________ .
Let A = {1, 2, 3} and B = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, 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, _____________________ .
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 ______________ .
Show that the relation R on the set Z of integers, given by R = {(a,b):2divides (a - b)} is an equivalence relation.
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).
Let A = {0, 1, 2, 3} and define a relation R on A as follows: R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}. Is R reflexive? symmetric? transitive?
Let Z be the set of integers and R be the relation defined in Z such that aRb if a – b is divisible by 3. Then R partitions the set Z into ______ pairwise disjoint subsets
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, transitive but not symmetric
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
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is ______.
Every relation which is symmetric and transitive is also reflexive.
Let A = {1, 2, 3, …. n} and B = {a, b}. Then the number of surjections from A into B is ____________.
The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R-1 is given by ____________.
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?
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}
- Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?
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?
A relation 'R' in a set 'A' is called reflexive, if
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 ______
Read the following passage:
|
An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. 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. |
Based on the above information, answer the following questions:
- How many relations are possible from B to G? (1)
- Among all the possible relations from B to G, how many functions can be formed from B to G? (1)
- Let R : B `rightarrow` B be defined by R = {(x, y) : x and y are students of the same sex}. Check if R is an equivalence relation. (2)
OR
A function f : B `rightarrow` G be defined by f = {(b1, g1), (b2, g2), (b3, g1)}. Check if f is bijective. Justify your answer. (2)
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)].
What should be checked to determine whether a relation is symmetric?

