Reflexive Relations

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. Reflexive and symmetric

2. Symmetric only

3. Transitive only

4. Antisymmetric only

Q.

Let $A=\left\{2,4,6,8\right\}$. A relation $R$ on $A$is defined by $R=\left\{\left(2,4\right),\left(4,2\right),\left(4,6\right),\left(6,4\right)\right\}$. Then $R$ is

1. Antisymmetric

2. Reflexive

3. Symmetric

4. Transitive

Q.

For $n,mϵN,n/m$means that $n$ is a factor of $m$, the relation $/$is

1. Reflexive and Symmetric

2. Transitive and Symmetric

3. Reflexive Transitive and Symmetric

4. Reflexive Transitive and not Symmetric.

Q. Let a relation R in the set R of real numbers be defined as (a, b) $ϵ$ R if and only if 1 + ab > 0 for all a, b $ϵ$ R. The
relation R is

1. None of these
2. Reflexive and symmetric
3. symmetric and transitive
4. an equivalence relation

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 $S$ be the set of all real numbers. Then the relation $R=\left\{\right(a,b):1+ab>0\}$ on S is

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

Q. Let R and S be two non – void relation in a set A. which of the following statements is false?

1. R and S transitive $\Rightarrow$ R $\cup$ S is not transitive
2. R and S symmetric $\Rightarrow$ R $\cup$ S is symmetric
3. R and S transitive $\Rightarrow$R $\cap$ S is transitive
4. R and S reflexive $\Rightarrow$ R $\cap$ S is reflexive

Q. R is relation over the set of integers and it is given by (x, y) $ϵ$ R $\iff$ R |x - y| $\le$ 1. Then, R is

1. Reflexive and transitive
2. reflexive and symmetric
3. Symmetric and transitive
4. an equivalence relation

Q. $N$ is the set of natural numbers. The relation $R$ is defined on $N\times N$ as follow $(a,b)R(c,d)\iff a+d=b+c$. Then, $R$ is

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

Q.

On the set $R$ of all real numbers, a relation $R$ is defined by $R=(a,b):1+ab>0$.Then $R$ is

1. Reflexive and symmetric only

2. Reflexive and Transitive only

3. Symmetric and Transitive only

4. An equivalence relation

Q. The following relation is defined on the set of real number:

1. symmetric
2. transitive
3. reflexive
4. none of these

Q. The relation 'less than' in the set of natural numbers is

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

Q. If $3x\equiv 5\left(mod7\right)$, then.

1. $x\equiv 2\left(mod7\right)$
2. $x\equiv 4\left(mod7\right)$
3. $x\equiv 3\left(mod7\right)$
4. None of these

Q.

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

Q. On the set $N$ of all natural numbers define the relation $R$ by $a$ and $b$ if and only if G.C.D. of $a$ and $b$ is $2$, then $R$ is

1. symmetric only
2. reflexive only
3. transitive only
4. equivalence