Reflexive Relations

Q.

Let $R$ be a reflexive relation of a finite set $A$ having $n$ elements and let there be $m$ ordered pairs in $R.$Then,

1. $m\ge n$

2. $m\le n$

3. $m=n$

4. None of these

Q. If $A=\{1,2,3\},$ then number of reflexive relations that can be defined on $A$ is

Q. Let a relation be defined on a set of functions defined on $R\to R$ such that R ={(f, g): f-g is an even function} then R is

1. Reflexive but not symmetric
2. Symmetric but not transitive
3. Equivalence relation
4. Not reflexive but symmetric & transitive

Q. Let $R$ be the relation on the set $R$ of all real numbers defined by $aRb$ iff $|a-b|\le 1.$ Then $R$ is

1. Symmetric only
2. Transitive only
3. Reflexive and symmetric
4. Anti-symmetric only

Q. Let R be the relation on the set of all real numbers defined by a R b iff $|a-b|\le 1$. Then R is

1. Reflexive and Symmetric
2. Symmetric only
3. Transitive only
4. Anti-symmetric only

Q. Let a relation $R$ on the set $N$ of natural numbers be defined as $(x,y)\iff x^2-4xy+3y^2=0\forall x,y\in N.$ Then the relation $R$ is

1. reflexive
2. symmetric
3. transitive
4. an equivalence relation

Q.

Define a reflexive relation.

Q.

Let R be a relation on the set N of natural numbers defined by nRm

⇔ n is a factor of m (i.e. n(m). Then R is

1. Reflexive and symmetric

2. Transitive and symmetric

3. Equivalence

4. Reflexive, transitive but not symmetric

Q.

Let R be the realtion on the set R of all real

numbers defined by a R b if |a-b| $\le$ 1. then R is

1. Reflexive and Symmetric

2. Symmetric only

3. Transitive only

4. Anti-symmetric only

Q. If $n\left(A\right)=m,m>0$, then number of reflexive relations from $A$ to $A$ is

1. $2^m$
2. $2^{m^2}$
3. $2^{m^2+m}$
4. $2^{m^2-m}$