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Byju's Answer
Standard XII
Mathematics
Equivalence Class
The binary re...
Question
The binary relation
S
=
f
(empty set)
on set
A
=
{
1
,
2
,
3
}
is
A
Neither reflexive nor symmetric
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B
Symmetric and reflexive
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C
Transitive and reflexive
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D
Transitive and symmetric
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Solution
The correct option is
D
Transitive and symmetric
The empty relation on any set is always transitive and symmetric but not reflexive.
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2
Similar questions
Q.
Let
R
be the set of all binary relations on the set
{
1
,
2
,
3
}
. Suppose a relation is chosen from
R
at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is
Q.
The number of binary operations on the set
{
1
,
2
,
3
}
is _________.
Q.
Relation
S
=
{
(
1
,
2
)
,
(
2
,
1
)
,
(
2
,
3
)
}
is defined on the set
{
1
,
2
,
3
}
is _________.
Q.
On set
A
=
{
1
,
2
,
3
}
, relation
R
and
S
are given by
R
=
{
(
1
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
,
(
1
,
2
)
,
(
2
,
1
)
}
S
=
{
(
1
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
,
(
1
,
3
)
,
(
3
,
1
)
}
Then.
Q.
The number of binary relations on a set with
n
elements is
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