Symmetric Relations

Q.

Let $P=\left\{(x,y)|x^2+y^2=1;x,y\in R\right\}$. then $P$ is

1. Reflexive

2. Symmetric

3. Transitive

4. Antisymmetric

Q. if A and B are any two non empty sets and A is proper subset of B. If n(A)=5 then minimum possible value of n(A*B) IS? *=SYMMETRIC DIFFERENCE.

Q. If $A=\left\{x,y,z\right\}$, then the relation $R=\left\{\right(x,x),(y,y),(z,z),(z,x),(x,z\left)\right\}$ is:

1. Symmetric
2. Reflexive
3. Transitive
4. Equivalence

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 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. symmetric
3. transitive
4. an equivalence

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 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.

Which of the following relations is only symmetric?

1. “less than equal to” on a set of Real numbers

2. “is a multiple of ” on the set of positive integers

3. “is perpendicular to” on a set of a coplanar lines

4. “is the father of ” on a set of family members.