मराठी

Mark the Correct Alternative in the Following Question: the Maximum Number of Equivalence Relations on the Set a = {1, 2, 3} is _______________ . - Mathematics

Advertisements
Advertisements

प्रश्न

Mark the correct alternative in the following question:

The maximum number of equivalence relations on the set A = {1, 2, 3} is _______________ .

पर्याय

  • 1

  • 2

  • 3

  • 5

MCQ

उत्तर

Hence, The maximum number of equivalence relations on the set A = {1, 2, 3} is 5.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations - Exercise 1.4 [पृष्ठ ३३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 1 Relations
Exercise 1.4 | Q 29 | पृष्ठ ३३

संबंधित प्रश्‍न

determination of whether the following relations are reflexive, symmetric, and transitive:

Relation R in the set N of natural numbers defined as

R = {(x, y): y = x + 5 and x < 4}


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


Let L be the set of all lines in 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.


Three relations R1, R2 and R3 are defined on a set A = {a, b, c} as follows:
R1 = {(a, a), (a, b), (a, c), (b, b), (b, c), (c, a), (c, b), (c, c)}
R2 = {(a, a)}
R3 = {(b, c)}
R4 = {(a, b), (b, c), (c, a)}.

Find whether or not each of the relations R1, R2, R3, R4 on A is (i) reflexive (ii) symmetric and (iii) transitive.


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


The following relation is defined on the set of real numbers.
aRb if a – b > 0

Find whether relation is reflexive, symmetric or transitive.


The following relation is defined on the set of real numbers.

aRb if 1 + ab > 0

Find whether relation is reflexive, symmetric or transitive.


If = {1, 2, 3, 4} define relations on A which have properties of being reflexive, symmetric and transitive ?


Let A = {abc} and the relation R be defined on A as follows: R = {(aa), (bc), (ab)}. Then, write minimum number of ordered pairs to be added in R to make it reflexive and transitive.


Defines a relation on :
  x > y, x, y ∈  N

Determine the above relation is reflexive, symmetric and transitive.


Defines a relation on N:

x + 4y = 10, x, y ∈ N

Determine the above relation is reflexive, symmetric and 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.


If R and S are transitive relations on a set A, then prove that R ∪ S may not be a transitive relation on A.


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


Let R = {(a, a3) : a is a prime number less than 5} be a relation. Find the range of R.


Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(ab) : | a2b| < 8}. Write as a set of ordered pairs.


R is a relation on the set Z of integers and it is given by
(x, y) ∈ R ⇔ | x − y | ≤ 1. Then, R is ______________ .


Let R be a relation on N defined by x + 2y = 8. The domain of R is _______________ .


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


Show that the relation R defined by (a, b)R(c,d) ⇒ a + d = b + c   on the A x A  , where A =  {1, 2,3,...,10}  is an equivalence relation. Hence write the equivalence class [(3, 4)]; a, b, c,d ∈ A.


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


Let A = {6, 8} and B = {1, 3, 5}.
Let R = {(a, b)/a∈ A, b∈ B, a – b is an even number}. Show that R is an empty relation from A to B.


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


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 A = {1, 2, 3, ... 9} and R be the relation in A × A defined by (a, b) R(c, d) if a + d = b + c for (a, b), (c, d) in A × A. Prove that R is an equivalence relation and also obtain the equivalent class [(2, 5)]


The maximum number of equivalence relations on the set A = {1, 2, 3} are ______.


Let R be the relation on N defined as by x + 2 y = 8 The domain of R is ____________.


Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ____________.


Let us define a relation R in R as aRb if a ≥ b. Then R is ____________.


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


A relation 'R' in a set 'A' is called a universal relation, if each element of' A' is related to :-


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 ______.


Read the following passage:

An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. 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} and G = {g1, g2}, where B represents the set of Boys selected and G the set of Girls selected for the final race.

Based on the above information, answer the following questions:

  1. How many relations are possible from B to G? (1)
  2. Among all the possible relations from B to G, how many functions can be formed from B to G? (1)
  3. Let R : B `rightarrow` B be defined by R = {(x, y) : x and y are students of the same sex}. Check if R is an equivalence relation. (2)
    OR
    A function f : B `rightarrow` G be defined by f = {(b1, g1), (b2, g2), (b3, g1)}. Check if f is bijective. Justify your answer. (2)

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×