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JEE Main Math Class 11 Sets Part 1 Questions
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© examsnet.com
Question : 4
Total: 51
Let
R
be a relation on
Z
×
Z
defined by
(
a
,
b
)
R
(
c
,
d
)
if and only if ad - bc is divisible by 5 . Then
R
is
[29-Jan-2024 Shift 1]
Reflexive and symmetric but not transitive
Reflexive but neither symmetric not transitive
Reflexive, symmetric and transitive
Reflexive and transitive but not symmetric
Validate
Solution:
👈: Video Solution
(
a
,
b
)
R
(
a
,
b
)
as
a
b
−
a
b
=
0
Therefore reflexive
Let
(
a
,
b
)
R
(
c
,
d
)
⇒
a
d
−
b
c
is divisible by 5
⇒
bc
−
ad
is divisible by
5
⇒
(
c
,
d
)
R
(
a
,
b
)
Therefore symmetric
Relation not transitive as
(
3
,
1
)
R
(
10
,
5
)
and
(
10
,
5
)
R
(
1
,
1
)
but
(
3
,
1
)
is not related to
(
1
,
1
)
© examsnet.com
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