Question
Let R be a relation defined in the set of real numbers by a R b 1 + ab > 0. Then R is-
- Equivalence relation
- Transitive
- Symmetric
- Anti-symmetric
The correct answer is: Symmetric
To find the type of relation R is.
Given relation is aRb is 1+ab>0,
Considering both a and b are real numbers,
We know that ab=ba,
aRb=1+ab>0=1+ba>0=bRa,
R is a symmetric relation.
Therefore, the given relation R is symmetric.
Related Questions to study
A and B are two sets having 3 and 4 elements respectively and having 2 elements in common. The number of relation which can be defined from A to B is
Therefore, the number of relations which can be defined from A to B are ..
A and B are two sets having 3 and 4 elements respectively and having 2 elements in common. The number of relation which can be defined from A to B is
Therefore, the number of relations which can be defined from A to B are ..
Let L denote the set of all straight lines in a plane. Let a relation R be defined by Then R is-
Hence, the relation R is symmetric.
Let L denote the set of all straight lines in a plane. Let a relation R be defined by Then R is-
Hence, the relation R is symmetric.
Let X={1,2,3,4} and Y={1,3,5,7,9} . Which of the following is relations from X to Y-
So the correct relations are R2 and R3.
Let X={1,2,3,4} and Y={1,3,5,7,9} . Which of the following is relations from X to Y-
So the correct relations are R2 and R3.
If Q=then-
Hence, is correct.
If Q=then-
Hence, is correct.
Let Aand =R-D, then the set D is
Therefore, set of D is .
Let Aand =R-D, then the set D is
Therefore, set of D is .
Which set is the subset of all given sets ?
Therefore, { } is a subset of all givens sets.
Which set is the subset of all given sets ?
Therefore, { } is a subset of all givens sets.
Let A and B be two sets such that n(A) = 70, n(B) = 60 and = 110. Then is equal to-
Therefore, n(A∩B) = 20
Let A and B be two sets such that n(A) = 70, n(B) = 60 and = 110. Then is equal to-
Therefore, n(A∩B) = 20
The shaded region in the given figure is
The shaded region in the given figure is
Which of the following are true ?
Therefore, from the given options, is true.
Which of the following are true ?
Therefore, from the given options, is true.
The set of intelligent students in a class is-
The set of intelligent students in a class is-
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A={1, 2, 5}, B = {6, 7} then is-
Therefore, A ⋂ B’ = A.
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A={1, 2, 5}, B = {6, 7} then is-
Therefore, A ⋂ B’ = A.
If , then is equal to-
Therefore, is equal to = A
If , then is equal to-
Therefore, is equal to = A