Symmetric Relations

Q. Let R be the relation defined on the set N of natural numbers by the relation xRy iff x + 2y = 5, then R is

माना प्राकृत संख्याओं के समुच्चय N पर परिभाषित एक संबंध R है, जो संबंध xRy द्वारा दिया गया है यदि और केवल यदि x + 2y = 5, तब R है

1. Symmetric
   
   सममित
2. Reflexive
   
   स्वतुल्य
3. An equivalence relation
   
   एक समतुल्य संबंध
4. Not reflexive
   
   स्वतुल्य नहीं

Q. 15. If the numbers of different reflexive relation on a set A is equal to the number of different symmetric relation on set A, then the number of element in A is ?

Q.

Let X be a family of sets and R be a relation on X defined by 'A is disjoint from B'. Then R is

1. Reflexive

2. Symmetric

3. Anti-symmetric

4. Transitive

Q.

Let R be the relation over the set of all straight lines in a plane such that

$l_{1}R{l}_2\iff l_1\perp l_2$. Then, R is

1. Reflexive

2. Transitive

3. An equivalence

4. Symmetric

Q. 35. Let h(x) = f(x)-1 . If f(x)+f(1-x) =2 for all x benlongs to R , then h(x) is symmetric about

Q. What is the general formula for number of symmetric relations of a set with n elements?

Q. Let $R$ be a relation on a set $A$ such that $R=R^{-1}$, then $R$ is

1. a reflexive relation
2. a symmetric relation
3. a transitive relation
4. None of the above