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प्रश्न
Show that the relation R on R defined as R = {(a, b): a ≤ b}, is reflexive, and transitive but not symmetric.
उत्तर
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 each of 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 in each case.
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
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
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.
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, symmetric and transitive ?
Defines a relation on N :
x + y = 10, x, y∈ N
Determine the above relation is reflexive, symmetric and transitive.
Defines a relation on N :
xy is square of an integer, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
Show that the relation R, defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have 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 A = {2, 3, 4}, B = {1, 3, 7} and R = {(x, y) : x ∈ A, y ∈ B and x < y} is a relation from A to B, then write R−1.
Define a reflexive relation ?
If a relation R is defined on the set Z of integers as follows:
(a, b) ∈ R ⇔ a2 + b2 = 25. Then, domain (R) is ___________
Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is _______________ .
The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is ___________________ .
Mark the correct alternative in the following question:
The maximum number of equivalence relations on the set A = {1, 2, 3} is _______________ .
If A = {a, b, c}, B = (x , y} find B × B.
Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6} Find (A × B) ∩ (A × C).
Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is ______.
Consider the set A = {1, 2, 3} and R be the smallest equivalence relation on A, then R = ______
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, symmetric and transitive
Let the relation R be defined in N by aRb if 2a + 3b = 30. Then R = ______.
Let A = { 2, 3, 6 } Which of the following relations on A are reflexive?
A relation R on a non – empty set A is an equivalence relation if it is ____________.
Given set A = {1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be ____________.
A relation S in the set of real numbers is defined as `"xSy" => "x" - "y" + sqrt3` is an irrational number, then relation S is ____________.
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.
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Find: `int (x + 1)/((x^2 + 1)x) dx`
The number of surjective functions from A to B where A = {1, 2, 3, 4} and B = {a, b} is
Statement 1: The intersection of two equivalence relations is always an equivalence relation.
Statement 2: The Union of two equivalence relations is always an equivalence relation.
Which one of the following is correct?
