Advertisements
Advertisements
प्रश्न
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?
उत्तर
R is reflexive and symmetric, but not transitive since for (1, 0) ∈ R and (0, 3) ∈ R whereas (1, 3) ∉ R
APPEARS IN
संबंधित प्रश्न
Given an example of a relation. Which is Reflexive and symmetric but not transitive.
Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is
(A) 1 (B) 2 (C) 3 (D) 4
Let A be the set of all human beings in a town at a particular time. Determine whether of the following relation is reflexive, symmetric and transitive :
R = {(x, y) : x and y live in the same locality}
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
Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.
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 N :
x > y, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
Defines a relation on N :
x + y = 10, x, y∈ N
Determine the above relation is reflexive, symmetric and transitive.
Write the identity relation on set A = {a, b, c}.
Define a symmetric relation ?
Let A = {0, 1, 2, 3} and R be a relation on A defined as
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}
Is R reflexive? symmetric? transitive?
Let the relation R be defined on N by aRb iff 2a + 3b = 30. Then write R as a set of ordered pairs
If A = {a, b, c}, B = (x , y} find A × B.
If A = {a, b, c}, B = (x , y} find A × A.
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 ______.
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
symmetric but neither reflexive nor 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)]
The maximum number of equivalence relations on the set A = {1, 2, 3} are ______.
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is ______.
Let A = { 2, 3, 6 } Which of the following relations on A are reflexive?
Let R be the relation on N defined as by x + 2 y = 8 The domain of R is ____________.
R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A, then R is ____________.
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 ____________.
Let the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by R = {(a, b) : |a – b| is a multiple of 4}. Then [1], the equivalence class containing 1, is:
A relation S in the set of real numbers is defined as `"xSy" => "x" - "y" + sqrt3` is an irrational number, then relation S 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 market research group conducted a survey of 2000 consumers and reported that 1720 consumers like product P1 and 1450 consumers like product P2. What is the least number that must have liked both the products?
A relation 'R' in a set 'A' is called reflexive, if
If f(x + 2a) = f(x – 2a), then f(x) is:
If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.