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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.
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उत्तर
संबंधित प्रश्न
Determine whether the following relation is reflexive, symmetric and transitive:
Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}.
Given an example of a relation. Which is Symmetric but neither reflexive nor transitive.
Let L be the set of all lines in the XY plane and R be the relation in L defined as R = {(L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.
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 and y live in the same locality}
Test whether the following relation R1 is (i) reflexive (ii) symmetric and (iii) transitive :
R1 on Q0 defined by (a, b) ∈ R1 ⇔ a = 1/b.
Give an example of a relation which is reflexive and symmetric but not transitive?
Give an example of a relation which is transitive but neither reflexive nor symmetric?
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.
Let S be a relation on the set R of all real numbers defined by
S = {(a, b) ∈ R × R : a2 + b2 = 1}
Prove that S is not an equivalence relation on R.
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}.
A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(x, y) : y is one half of x; x, y ∈ A} is a relation on A, then write R as a set of ordered pairs.
A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : x R y ⇔ x is relatively prime to y. Then, domain of R is ______________ .
Mark the correct alternative in the following question:
Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then, R is _____________ .
For the matrix A = `[(2,3),(5,7)]`, find (A + A') and verify that it is a symmetric matrix.
Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is ______.
Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if and only if l is perpendicular to m ∀ l, m ∈ L. Then R is ______.
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
symmetric but neither reflexive nor transitive
The following defines a relation on N:
x + 4y = 10 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)]
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ∀ a, b ∈ T. Then R is ______.
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is ______.
Let us define a relation R in R as aRb if a ≥ b. Then R is ______.
Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ____________.
Let A = {1, 2, 3, …. n} and B = {a, b}. Then the number of surjections from A into B is ____________.
Let R be the relation “is congruent to” on the set of all triangles in a plane is ____________.
The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R-1 is given by ____________.
If f(x + 2a) = f(x – 2a), then f(x) is:
