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Byju's Answer
Standard VII
Mathematics
Line Symmetry
Prove that th...
Question
Prove that the relation "is perpendicular to" on the set L of all straight lines in a plane is symmetric but neither reflexive nor transitive on L.
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Q.
Let
L
be the set of all lines in a plane and
R
be the relation in
L
defined as
R
=
{
(
L
1
,
L
2
)
:
L
1
⊥
L
2
}
. Show that
R
is symmetric but neither reflexive nor transitive.
Q.
The relation
R
on the set of natural numbers
N
is defined as
x
R
y
⟺
x
2
−
4
x
y
+
3
y
2
=
0
,
x
,
y
∈
N
then
R
is
Q.
The relation
R
=
{
(
1
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
,
(
1
,
2
)
,
(
2
,
3
)
,
(
1
,
3
)
}
on the set
A
=
{
1
,
2
,
3
}
is
Q.
Let
R
=
{
(
3
,
3
)
,
(
6
,
6
)
,
(
9
,
9
)
,
(
12
,
12
)
,
(
6
,
12
)
,
(
3
,
9
)
,
(
3
,
12
)
,
(
3
,
6
)
}
be a relation on the set
A
=
{
3
,
6
,
9
,
12
}
.
Then the relation is
Q.
Mark the correct alternative in the following question:
The relation S defined on the set R of all real number by the rule aSb iff a
≥
b is
(a) an equivalence relation
(b) reflexive, transitive but not symmetric
(c) symmetric, transitive but not reflexive
(d) neither transitive nor reflexive but symmetric
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