Advertisements
Advertisements
प्रश्न
Let us define a relation R in R as aRb if a ≥ b. Then R is ______.
विकल्प
An equivalence relation
Reflexive, transitive but not symmetric
Symmetric, transitive but not reflexive
Neither transitive nor reflexive but symmetric
उत्तर
Let us define a relation R in R as aRb if a ≥ b. Then R is reflexive, transitive but not symmetric.
Explanation:
Given that, aRb if a ≥ b
⇒ aRa
⇒ a ≥ a which is true.
Let aRb, a ≥ b, then b ≥ a which i not true,
So R is not symmetric.
But aRb and bRc
⇒ a ≥ b and b ≥ c
⇒ a ≥ c
Hence, R is transitive.
APPEARS IN
संबंधित प्रश्न
Let N denote the set of all natural numbers and R be the relation on N × N defined by (a, b) R (c, d) if ad (b + c) = bc (a + d). Show that R is an equivalence relation.
Given an example of a relation. Which is Reflexive and transitive but not symmetric.
Given an example of a relation. Which is Symmetric and transitive but not reflexive.
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 is father of and 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 reflexive and symmetric but not transitive ?
Defines a relation on N :
xy is square of an integer, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
m is said to be related to n if m and n are integers and m − n is divisible by 13. Does this define an equivalence relation?
Let Z be the set of all integers and Z0 be the set of all non-zero integers. Let a relation R on Z × Z0be defined as (a, b) R (c, d) ⇔ ad = bc for all (a, b), (c, d) ∈ Z × Z0,
Prove that R is an equivalence relation on Z × Z0.
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 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 R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is _______________ .
Mark the correct alternative in the following question:
The relation S defined on the set R of all real number by the rule aSb if a b is _______________ .
Mark the correct alternative in the following question:
The maximum number of equivalence relations on the set A = {1, 2, 3} is _______________ .
If f (x) = `(4x + 3)/(6x - 4) , x ≠ 2/3`, show that fof (x) = x for all ` x ≠ 2/3` . Also, find the inverse of f.
For the matrix A = `[(2,3),(5,7)]`, find (A + A') and verify that it is a symmetric matrix.
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 ______.
Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
a mapping from B to A
The following defines a relation on N:
x + 4y = 10 x, y ∈ N.
Determine which of the above relations are reflexive, symmetric and transitive.
Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is ______.
The maximum number of equivalence relations on the set A = {1, 2, 3} are ______.
Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. Then R is ______.
Let R be the relation on N defined as by x + 2 y = 8 The domain of R is ____________.
If f(x) = `1 - 1/"x", "then f"("f"(1/"x"))` ____________.
Let R be the relation “is congruent to” on the set of all triangles in a plane is ____________.
Given triangles with sides T1: 3, 4, 5; T2: 5, 12, 13; T3: 6, 8, 10; T4: 4, 7, 9 and a relation R inset of triangles defined as R = `{(Delta_1, Delta_2) : Delta_1 "is similar to" Delta_2}`. Which triangles belong to the same equivalence class?
If A is a finite set consisting of n elements, then the number of reflexive relations on A is
Which one of the following relations on the set of real numbers R is an equivalence relation?
If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.
