Advertisements
Advertisements
प्रश्न
Consider the 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 ______.
पर्याय
Symmetric but not transitive
Transitive but not symmetric
Neither symmetric nor transitive
Both symmetric and transitive
उत्तर
Consider the 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 transitive but not symmetric.
Explanation:
aRb ⇒ a is brother of b.
This does not mean b is also a brother of a as b can be a sister of a.
Thus, R is not symmetric.
aRb ⇒ a is brother of b.
and bRc ⇒ b is brother of c.
So, a is brother of c.
Therefore, R is transitive.
APPEARS IN
संबंधित प्रश्न
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 of points in a plane given by R = {(P, Q): distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P ≠ (0, 0) is the circle passing through P with origin as centre.
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.
Given a non-empty set X, consider P (X), which is the set of all subsets of X. Define the relation R in P(X) as follows:
For subsets A, B in P(X), ARB if and only if A ⊂ B. Is R an equivalence relation on P(X)? Justify your answer.
Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is
(A) 1
(B) 2
(C) 3
(D) 4
Let A be the set of all human beings in a town at a particular time. Determine whether of the following relation is reflexive, symmetric and transitive :
R = {(x, y) : x and y live in the same locality}
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.
Show that the relation R defined by R = {(a, b) : a – b is divisible by 3; a, b ∈ Z} is an equivalence relation.
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.
Write the identity relation on set A = {a, b, c}.
Let A = {3, 5, 7}, B = {2, 6, 10} and R be a relation from A to B defined by R = {(x, y) : x and y are relatively prime}. Then, write R and R−1.
Define a transitive relation ?
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 = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R 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:
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 _______________ .
Mark the correct alternative in the following question:
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 for all a, b T. Then, R is ____________ .
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 ______.
Consider the set A = {1, 2, 3} and R be the smallest equivalence relation on A, then R = ______
Let Z be the set of integers and R be the relation defined in Z such that aRb if a – b is divisible by 3. Then R partitions the set Z into ______ pairwise disjoint subsets
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, transitive but not symmetric
The following defines a relation on N:
x is greater than y, x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.
Let us define a relation R in R as aRb if a ≥ b. Then R is ______.
R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A, then R is ____________.
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 ____________.
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?
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}
- Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?
Which one of the following relations on the set of real numbers R is an equivalence relation?
Let L be a set of all straight lines in a plane. The relation R on L defined as 'perpendicular to' is ______.
