हिंदी

Let A = {A, B, C} and the Relation R Be Defined On A As Follows: R = {(A, A), (B, C), (A, B)}. Then, Write Minimum Number of Ordered Pairs to Be Added In R To Make It Reflexive and Transitive.

Advertisements
Advertisements

प्रश्न

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.

एक पंक्ति में उत्तर
योग
Advertisements

उत्तर

We have,
 A = {abc} and R = {(aa), (bc), (ab)}

R can be a reflexive relation only when elements (bb) and (cc) are added to it

R can be a transitive relation only when the element (ac) is added to it 

So, the minmum number of ordered pairs to be added in R is 3.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations - Exercise 1.1 [पृष्ठ ११]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 1 Relations
Exercise 1.1 | Q 17 | पृष्ठ ११

संबंधित प्रश्न

If R=[(x, y) : x+2y=8] is a relation on N, write the range of R.


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.


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


Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b) : |a − b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.


Show that the relation R defined in the set A of all polygons as R = {(P1, P2): P1 and P2 have 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 R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.


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 wife of y}


Test whether the following relation R3 is (i) reflexive (ii) symmetric and (iii) transitive:

R3 on R is defined by (a, b) ∈ R3 `⇔` a2 – 4ab + 3b2 = 0.


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


Defines a relation on N:

x + 4y = 10, x, y ∈ N

Determine the above relation is reflexive, symmetric and transitive.


Prove that the relation R on Z defined by
(a, b) ∈ R ⇔ a − b is divisible by 5
is an equivalence relation on Z.


State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive ?


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


If A = {a, b, c}, then the relation R = {(b, c)} on A is _______________ .


The relation 'R' in N × N such that
(a, b) R (c, d) ⇔ a + d = b + c is ______________ .


R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x − 3. Then, R−1 is ______________ .


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


Mark the correct alternative in the following question:

For real numbers x and y, define xRy if `x-y+sqrt2` is an irrational number. Then the relation R is ___________ .


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


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


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


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


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


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


Let A = { 2, 3, 6 } Which of the following relations on A are reflexive?


Let A = {1, 2, 3}, then the domain of the relation R = {(1, 1), (2, 3), (2, 1)} defined on A is ____________.


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


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


Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is ____________.


A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever


Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}

  • Mr. Shyam exercised his voting right in General Election-2019, then Mr. Shyam is related to which of the following?

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


If A is a finite set consisting of n elements, then the number of reflexive relations on A is


Let R = {(a, b): a = a2} for all, a, b ∈ N, then R salifies.


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 ______


Statement 1: The intersection of two equivalence relations is always an equivalence relation.

Statement 2: The Union of two equivalence relations is always an equivalence relation.

Which one of the following is correct?


A relation \(R\) on \(A\) is reflexive when which condition holds?


A relation \(R\) is symmetric if which condition is satisfied?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×