English

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

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

RD Sharma Mathematics [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 A of human beings in a town at a particular time given by R = {(x, y) : x is exactly 7 cm taller than y}.


The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*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 live in the same locality}


Give an example of a relation which is symmetric but neither reflexive nor transitive?


Let n be a fixed positive integer. Define a relation R on Z as follows:
(a, b) ∈ R ⇔ a − b is divisible by n.
Show that R 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?


Let R be the relation defined on the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.


Write the smallest reflexive relation on set A = {1, 2, 3, 4}.


If R = {(x, y) : x + 2y = 8} is a relation on N by, then write the range of R.


If A = {2, 3, 4}, B = {1, 3, 7} and R = {(x, y) : x ∈ A, y ∈ B and x < y} is a relation from A to B, then write R−1.


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.


A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(xy) : y is one half of xxy ∈ A} is a relation on A, then write R as a set of ordered pairs.


Let R be a relation on the set N given by
R = {(a, b) : a = b − 2, b > 6}. Then,


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 = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by 'x is greater than y'. The range of R is ______________ .


If A = {1, 2, 3}, then a relation R = {(2, 3)} on A is _____________ .


The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is ___________________ .


S is a relation over the set R of all real numbers and it is given by (a, b) ∈ S ⇔ ab ≥ 0. Then, S 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 S in the set A = [x ∈ Z : 0 ≤ x ≤ 12] given by S = [(a, b) : a, b ∈ Z, ∣a − b∣ is divisible by 3] is an equivalence relation.


Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find (A × B) ∪ (A × C).


Write the relation in the Roster form and hence find its domain and range :
R1 = {(a, a2) / a is prime number less than 15}


In the set of natural numbers N, define a relation R as follows: ∀ n, m ∈ N, nRm if on division by 5 each of the integers n and m leaves the remainder less than 5, i.e. one of the numbers 0, 1, 2, 3 and 4. Show that R is equivalence relation. Also, obtain the pairwise disjoint subsets determined by R


Consider the set A = {1, 2, 3} and the relation R = {(1, 2), (1, 3)}. R is a transitive relation.


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


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 ______.


Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : |a2 – b2| < 8. Then R is given by ______.


Which of the following is not an equivalence relation on I, the set of integers: x, y


Let A = {1, 2, 3, 4, 5, 6} Which of the following partitions of A correspond to an equivalence relation on A?


Let A = {1, 2, 3, …. n} and B = {a, b}. Then the number of surjections from A into B 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 ____________.


Given set A = {1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be ____________.


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 ____________.

If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘x is smaller than y’. The range of R is ____________.


Find: `int (x + 1)/((x^2 + 1)x) dx`


There are 600 student in a school. If 400 of them can speak Telugu, 300 can speak Hindi, then the number of students who can speak both Telugu and Hindi is:


Which of the following is/are example of symmetric


Define the relation R in the set N × N as follows:

For (a, b), (c, d) ∈ N × N, (a, b) R (c, d) if ad = bc. Prove that R is an equivalence relation in N × N.


Let f(x)= ax2 + bx + c be such that f(1) = 3, f(–2) = λ and f(3) = 4. If f(0) + f(1) + f(–2) + f(3) = 14, then λ is equal to ______.


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 ______


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×