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Test Index
JEE Main Math Class 11 Relations and Functions Part 2 Questions
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© examsnet.com
Question : 58
Total: 95
The minimum number of elements that must be added to the relation
R
=
{
(
a
,
b
)
,
(
b
,
c
)
}
on the set
{
a
,
b
,
c
}
so that it becomes symmetric and transitive is:
[30-Jan-2023 Shift 1]
4
7
5
3
Validate
Solution:
For Symmetric
(
a
,
b
)
,
(
b
,
c
)
∈
R
⇒
(
b
,
a
)
,
(
c
,
b
)
∈
R
For Transitive
(
a
,
b
)
,
(
b
,
c
)
∈
R
⇒
(
a
,
c
)
∈
R
Now
1. Symmetric
∴
(
a
,
c
)
∈
R
⇒
(
c
,
a
)
∈
R
2. Transitive
∴
(
a
,
b
)
,
(
b
,
a
)
∈
R
⇒
(
a
,
a
)
∈
R
&
(
b
,
c
)
,
(
c
,
b
)
∈
R
⇒
(
b
,
b
)
&
(
c
,
c
)
∈
R
∴
Elements to be added
{
(
b
,
a
)
(
c
,
b
)
(
a
,
c
)
(
c
,
a
)
,
(
a
,
a
)
(
b
,
b
)
(
c
,
c
)
}
Number of elements to be added
=
7
© examsnet.com
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