Symmetric Relations

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

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

Q.

Let P = {(x, y) $x^2+y^2=1,x,y\in R\}$. Then P is.

1. Reflexive

2. Symmetric

3. Transitive

4. Anti-symmetric

Q. Let R be the relation over the set of straight lines of a plane, such that $l_{1}R{l}_2\iff l_1\pm l_2$ . Then, R is

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

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

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

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

Q. Let R be the relation over the set of straight lines of a plane, such that $l_{1}R{l}_2\iff l_1\pm l_2$ . Then, R is

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