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Mathematics
Problem
14. Let L be the set of all lines in XY plane and R be the relation in L defined as
R
=
{
(
L
1
,
L
2
)
:
L
1
\mathrm{R}=\left\{\left(\mathrm{L}_{1}, \mathrm{~L}_{2}\right): \mathrm{L}_{1}\right.
R
=
{
(
L
1
,
L
2
)
:
L
1
is parallel to
L
2
}
\left.\mathrm{L}_{2}\right\}
L
2
}
. Show that R is an equivalence relation. Find the set of all lines related to the line
y
=
2
x
+
4
y=2 x+4
y
=
2
x
+
4
. a.
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