Advertisements
Advertisements
प्रश्न
Defines a relation on N :
x > y, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
Advertisements
उत्तर
We have,
R = {(x, y) : x > y, x, y ∈ N}
As, x = x ∀x ∈ N
⇒ (x,x) ∉ R
So, R is not a reflexive relation
Let (x,y) ∈ R
⇒ x > y
but y < x
⇒ (y,x) ∉ R
So, R is not a symmeteric relation
Let (x,y)∈R and (y,z) ∈ R
⇒ x > y and y > z
⇒ x > z
⇒ (x,z) ∈ R
So, R is a transitive relation
APPEARS IN
संबंधित प्रश्न
Determine whether the following relation is reflexive, symmetric and transitive:
Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer}.
Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or transitive.
Show that 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.
Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.
An integer m is said to be related to another integer n if m is a multiple of n. Check if the relation is symmetric, reflexive and transitive.
Show that the relation '≥' on the set R of all real numbers is reflexive and transitive but not symmetric ?
Give an example of a relation which is symmetric and transitive but not reflexive?
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 R be a relation on the set A of ordered pair of integers defined by (x, y) R (u, v) if xv = yu. Show that R is an equivalence relation.
Let O be the origin. We define a relation between two points P and Q in a plane if OP = OQ. Show that the relation, so defined is an equivalence relation.
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.
Let C be the set of all complex numbers and C0 be the set of all no-zero complex numbers. Let a relation R on C0 be defined as
`z_1 R z_2 ⇔ (z_1 -z_2)/(z_1 + z_2)` is real for all z1, z2 ∈ C0.
Show that R is an equivalence relation.
Define a reflexive relation ?
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.
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 the relation over the set of all straight lines in a plane such that l1 R l2 ⇔ l 1⊥ l2. Then, R is _____________ .
If A = {a, b, c}, then the relation R = {(b, c)} on A is _______________ .
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 ______________ .
Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. 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, _____________________ .
The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is ___________________ .
Mark the correct alternative in the following question:
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 for all a, b T. Then, R is ____________ .
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?
Consider the set A = {1, 2, 3} and R be the smallest equivalence relation on A, then R = ______
Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
a mapping from A to B which is not injective
The following defines a relation on N:
x y is square of an integer x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.
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 A = {1, 2, 3}, then the domain of the relation R = {(1, 1), (2, 3), (2, 1)} defined on A is ____________.
Let A = {1, 2, 3, 4, 5, 6} Which of the following partitions of A correspond to an equivalence relation on A?
Let `"f"("x") = ("x" - 1)/("x" + 1),` then f(f(x)) is ____________.
If f(x) = `1 - 1/"x", "then f"("f"(1/"x"))` ____________.
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 ____________.
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}
- Let R ∶ B → B be defined by R = {(x, y): y is divisible by x} is ____________.
The number of surjective functions from A to B where A = {1, 2, 3, 4} and B = {a, b} is
A relation in a set 'A' is known as empty relation:-
If f(x + 2a) = f(x – 2a), then f(x) is:
Let A = {3, 5}. Then number of reflexive relations on A is ______.
Which statement defines a Universal Relation?
A relation \(R\) on \(A\) is reflexive when which condition holds?
