English

If A = {1, 2, 3, 4} Define Relations On A Which Have Properties of Being Symmetric but Neither Reflexive Nor Transitive ?

Advertisements
Advertisements

Question

If = {1, 2, 3, 4} define relations on A which have properties of being symmetric but neither reflexive nor transitive ?

Sum
Advertisements

Solution

The relation on A having properties of being symmetric, but neither reflexive nor transitive is
R = {(1, 2), (2, 1)}
The relation R on A is neither reflexive nor transitive, but symmetric.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Relations - Exercise 1.1 [Page 11]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 1 Relations
Exercise 1.1 | Q 9.2 | Page 11

RELATED QUESTIONS

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}.


Determine whether the following relation is reflexive, symmetric and transitive:

Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x}.


Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.


Given an example of a relation. Which is reflexive and transitive but not symmetric.


Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is ______.


The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*4


Test whether the following relation R1 is  (i) reflexive (ii) symmetric and (iii) transitive :

R1 on Q0 defined by (a, b) ∈ R1 ⇔ = 1/b.


Let R be a relation defined on the set of natural numbers N as
R = {(xy) : x N, 2x + y = 41}
Find the domain and range of R. Also, verify whether R is (i) reflexive, (ii) symmetric (iii) transitive.


Give an example of a relation which is reflexive and symmetric but not transitive?


Give an example of a relation which is reflexive and transitive but not symmetric?


If R and S are relations on a set A, then prove that R is reflexive and S is any relation ⇒ R ∪ S is reflexive ?


If R = {(x, y) : x2 + y2 ≤ 4; x, y ∈ Z} is a relation on Z, write the domain of R.


Define an equivalence relation ?


Let the relation R be defined on N by aRb iff 2a + 3b = 30. Then write R as a set of ordered pairs


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 A = {1, 2, 3}. Then, the number of equivalence relations containing (1, 2) 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 _______________ .


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.


Show that the relation R on R defined as R = {(a, b): a ≤ b}, is reflexive, and transitive but not symmetric.


If A = {a, b, c}, B = (x , y} find A × B.


For real numbers x and y, define xRy if and only if x – y + `sqrt(2)` is an irrational number. Then the relation R is ______.


Let n be a fixed positive integer. Define a relation R in Z as follows: ∀ a, b ∈ Z, aRb if and only if a – b is divisible by n. Show that R is an equivalance relation


If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, transitive but not symmetric


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


Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
a mapping from B to A


Give an example of a map which is not one-one but onto


The following defines a relation on N:
x + y = 10, x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.


Let R be the relation on N defined as by x + 2 y = 8 The domain of 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 S = {1, 2, 3, 4, 5} and let A = S x S. Define the relation R on A as follows:
(a, b) R (c, d) iff ad = cb. Then, R is ____________.


Total number of equivalence relations defined in the set S = {a, b, c} 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?


Given set A = {a, b, c}. An identity relation in set A 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


On the set N of all natural numbers, define the relation R by a R b, if GCD of a and b is 2. Then, R is


In a group of 52 persons, 16 drink tea but not coffee, while 33 drink tea. How many persons drink coffee but not tea?


Which of the following is/are example of symmetric


Given a non-empty set X, define the relation R in P(X) as follows:

For A, B ∈ P(X), (4, B) ∈ R iff A ⊂ B. Prove that R is reflexive, transitive and not symmetric.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×