Advertisements
Advertisements
प्रश्न
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 ____________ .
पर्याय
reflexive but not symmetric
transitive but not symmetric
equivalence
none of these
Advertisements
उत्तर
Hence, R is equivalence.
APPEARS IN
संबंधित प्रश्न
If R=[(x, y) : x+2y=8] is a relation on N, write the range of R.
Determine whether the following relation is reflexive, symmetric and transitive:
Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as R = {(x, y) : 3x − y = 0}.
Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the point P from the origin is the same as the distance of the point Q from the origin} is an equivalence relation. Further, show that the set of all points related to a point P ≠ (0, 0) is the circle passing through P with the origin as its centre.
Show that the relation R defined in the set A of all polygons as R = {(P1, P2): P1 and P2have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?
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 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 work at the same place}
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
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.
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 A = {1, 2, 3} and R = {(1, 2), (1, 1), (2, 3)} be a relation on A. What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A.
Defines a relation on N:
x + 4y = 10, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
Write the domain of the relation R defined on the set Z of integers as follows:-
(a, b) ∈ R ⇔ a2 + b2 = 25
Let R be a relation on the set N given by
R = {(a, b) : a = b − 2, b > 6}. Then,
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 be the relation over the set of all straight lines in a plane such that l1 R l2 ⇔ l 1⊥ l2. Then, R is _____________ .
Let A = {1, 2, 3}. Then, the number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive 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 ______________ .
R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x − 3. Then, R−1 is ______________ .
In the set Z of all integers, which of the following relation R is not an equivalence relation ?
Mark the correct alternative in the following question:
Consider a 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 _____________ .
For the matrix A = `[(2,3),(5,7)]`, find (A + A') and verify that it is a symmetric matrix.
If A = {a, b, c}, B = (x , y} find B × B.
Consider the set A = {1, 2, 3} and the relation R = {(1, 2), (1, 3)}. R is a transitive relation.
Let R be relation defined on the set of natural number N as follows:
R = {(x, y): x ∈N, y ∈N, 2x + y = 41}. Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive
Give an example of a map which is not one-one but onto
Give an example of a map which is neither one-one nor onto
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.
The following defines a relation on N:
x + 4y = 10 x, y ∈ N.
Determine which of the above relations are reflexive, symmetric and transitive.
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is ______.
Every relation which is symmetric and transitive is also reflexive.
Let A = { 2, 3, 6 } Which of the following relations on A are reflexive?
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 ____________.
An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.
Ravi decides to explore these sets for various types of relations and functions.
- Ravi wishes to form all the relations possible from B to G. How many such relations are possible?
The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has nontrivial solution is
The relation > (greater than) on the set of real numbers is
A relation 'R' in a set 'A' is called reflexive, if
Let R = {(x, y) : x, y ∈ N and x2 – 4xy + 3y2 = 0}, where N is the set of all natural numbers. Then the relation R is ______.
Let A = {1, 2, 3, 4} and let R = {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is ______.
