Let A be the set of all lines in the plane. Define a relation R on A as follows. For every l1 and l2 in A, l1 R l2 ⇔ l1 is parallel to l2. (Assume that a line is parallel to itself). Which of the following is true for R? A. R is reflexive.
B. R is symmetric.
C. R is transitive.
D. R is neither reflexive, symmetric, nor transitive.

Hence, the relation R is a reflexive, symmetric and transitive relation.

Given :

A be the set of all lines in the plane and R is a relation on set A.

To find :

Which type of relation R on set A.

Explanation :

A relation R on a set A is called reflexive relation if every then .

So, the relation R is a reflexive relation because a line always parallels to itself.

A relation R on a set A is called Symmetric relation if then for all .

So, the relation R is a symmetric relation because if a line is parallel to the line the always the line is parallel to the line .

A relation R on a set A is called transitive relation if and then for all .

So, the relation R is a transitive relation because if a line s parallel to the line and the line is parallel to the line then the always line is parallel to the line .

Therefore the relation R is a reflexive, symmetric and transitive relation.