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Byju's Answer
Standard XII
Mathematics
Definition of Functions
Given the rel...
Question
Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, add a minimum number of ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.
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Solution
R = {(1, 2), (2, 3)}
For
R
to
be
reflexive
it
must
have
(
1
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
.
For
R
to
be
symmetric
,
all
the
ordered
pairs
upon
interchanging
the
elements
must
be
present
in
R
.
Therefore
,
R
must
contain
2
,
1
and
3
,
2
,
3
,
1
,
1
,
3
.
Finally
,
for
R
to
be
transitive
,
it
must
contain
1
,
3
.
Hence, the number of ordered pairs to be added to R is 7, i.e. (1, 1), (2, 2), (3, 3), (1, 3), (3, 1), (2, 1), (3, 2).
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