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Answer:
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.