Advertisements
Advertisements
प्रश्न
Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.
पर्याय
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
Given that, R = {(3, 1), (1, 3), (3, 3)} be defined on the set A = {1, 2,
Since (1, 1) ∉ R, R is not reflexive.
Since (3, 1) ∈ R ⇒ (1, 3) ∈ R, R is symmetric.
Since, (1, 3) ∈ R, (3, 1) ∈ R
But (1, 1) ∉ R
Hence, R is not transitive.
APPEARS IN
संबंधित प्रश्न
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 is exactly 7 cm taller than y}
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.
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 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.
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]
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
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?
Let R be a relation defined on the set of natural numbers N as
R = {(x, y) : x, y ∈ N, 2x + y = 41}
Find the domain and range of R. Also, verify whether R is (i) reflexive, (ii) symmetric (iii) 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?
Defines a relation on N :
x > y, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
Let Z be the set of integers. Show that the relation
R = {(a, b) : a, b ∈ Z and a + b is even}
is an equivalence relation on Z.
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?
Show that the relation R on 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.
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 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 R and S are relations on a set A, then prove that R and S are symmetric ⇒ R ∩ S and R ∪ S are symmetric ?
Write the identity relation on set A = {a, b, c}.
Define an equivalence relation ?
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?
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 A = {2, 3, 4, 5, ..., 17, 18}. Let '≃' be the equivalence relation on A × A, cartesian product of Awith itself, defined by (a, b) ≃ (c, d) if ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is _______________ .
Let R be a relation on N defined by x + 2y = 8. The domain of R is _______________ .
If R is the largest equivalence relation on a set A and S is any relation on A, then _____________ .
Let A = {1, 2, 3}. Then, the number of equivalence relations containing (1, 2) 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 ____________ .
If A = {a, b, c}, B = (x , y} find A × B.
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?
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
An integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.
The relation R on the set A = {1, 2, 3} defined as R = {{1, 1), (1, 2), (2, 1), (3, 3)} is reflexive, symmetric and transitive.
Let A = {1, 2, 3, 4, 5, 6} Which of the following partitions of A correspond to an equivalence relation on A?
A relation S in the set of real numbers is defined as `"xSy" => "x" - "y" + sqrt3` is an irrational number, then relation S 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.
- Let R: B → B be defined by R = {(x, y): x and y are students of same sex}, Then this relation R is ____________.
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
Let R = {(a, b): a = a2} for all, a, b ∈ N, then R salifies.
Let R1 and R2 be two relations defined as follows :
R1 = {(a, b) ∈ R2 : a2 + b2 ∈ Q} and
R2 = {(a, b) ∈ R2 : a2 + b2 ∉ Q}, where Q is the set of all rational numbers. Then ______
lf A = {x ∈ z+ : x < 10 and x is a multiple of 3 or 4}, where z+ is the set of positive integers, then the total number of symmetric relations on A is ______.
