Advertisements
Advertisements
प्रश्न
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.
विकल्प
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
Given that, R = {(1, 1), (1, 2), (2, 1), (3, 3)}
(2, 2) ∉ R
So, R is not reflexive
APPEARS IN
संबंधित प्रश्न
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. Also, obtain the equivalence class [(2, 5)].
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}.
Given an example of a relation. Which is Symmetric but neither reflexive nor transitive.
Given an example of a relation. Which is Symmetric and transitive but not reflexive.
Let R be the relation in the set N given by R = {(a, b) : a = b − 2, b > 6}. 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 father of and y}
The following relation is defined on the set of real numbers. aRb if |a| ≤ b
Find whether relation is reflexive, symmetric or 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 reflexive and symmetric but not transitive?
Let A = {1, 2, 3} and R = {(1, 2), (1, 1), (2, 3)} be a relation on A. What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A.
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.
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.
A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(x, y) : y is one half of x; x, y ∈ A} is a relation on A, then write R as a set of ordered pairs.
Let R = {(a, a3) : a is a prime number less than 5} be a relation. Find the range of R.
The relation R defined on the set A = {1, 2, 3, 4, 5} by
R = {(a, b) : | a2 − b2 | < 16} is given by ______________ .
If A = {a, b, c}, then the relation R = {(b, c)} on A 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 _______________ .
A relation ϕ from C to R is defined by x ϕ y ⇔ | x | = y. Which one is correct?
Let A = {1, 2, 3}. Then, the number of equivalence relations containing (1, 2) is ______.
Mark the correct alternative in the following question:
Consider a non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then, R is _____________ .
Show that the relation R on R defined as R = {(a, b): a ≤ b}, is reflexive, and transitive but not symmetric.
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.
The following defines a relation on N:
x + y = 10, 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 A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. Then R is ______.
Let the relation R be defined in N by aRb if 2a + 3b = 30. Then R = ______.
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.
Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ____________.
If A is a finite set containing n distinct elements, then the number of relations on A is equal to ____________.
A relation R in set A = {1, 2, 3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A?
Given set A = {a, b, c}. An identity relation in set A 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 relation > (greater than) on the set of real numbers is
Which of the following is/are example of symmetric
If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.
