Let 
be the set of all straight lines in the Euclidean plane. Two lines 
and 
are said to be related by the relation 
iff 
is parallel to 
. Then, the relation 
is
Text Solution
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(a, b, c, d)
Relation 
on the set of all straight lines in the plane is of parallel line.
line is parallel to itself. So, 
is reflexive.
If 
is parallel to 
, then 
is parallel to 
.
is symmetric relation. 
Let 
is parallel to 
and 
is parallel to 
.
Then, 
is parallel to 
.
is transitive relation.
So, 
is an equivalence relation.
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