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JEE Main Math Class 11 Sets Part 1 Questions
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© examsnet.com
Question : 12
Total: 51
Consider the relations
R
1
and
R
2
defined as
a
R
1
b
⇔
a
2
+
b
2
=
1
for all
a
,
b
,
∈
R
and
(
a
,
b
)
R
2
(
c
,
d
)
⇔
a
+
d
=
b
+
c
for all
(
a
,
b
)
,
(
c
,
d
)
∈
N
×
N
. Then
[1-Feb-2024 Shift 2]
Only
R
1
is an equivalence relation
Only
R
2
is an equivalence relation
R
1
and
R
2
both are equivalence relations
Neither
R
1
nor
R
2
is an equivalence relation
Validate
Solution:
👈: Video Solution
a
R
1
b
⇔
a
2
+
b
2
=
1
;
a
,
b
∈
R
(
a
,
b
)
R
2
(
c
,
d
)
⇔
a
+
d
=
b
+
c
;
(
a
,
b
)
,
(
c
,
d
)
∈
N
for
R
1
: Not reflexive symmetric not transitive
for
R
2
:
R
2
is reflexive, symmetric and transitive
Hence only
R
2
is equivalence relation.
© examsnet.com
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