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Byju's Answer
Standard XII
Mathematics
Domain
Let A= 2, 3...
Question
Let
A
=
{
2
,
3
,
5
,
7
,
10
}
show that the relation
(i)
R
1
is A defined as "is equal to" is an identify relation. (ii)
R
2
is A defined as "difference is an integer" is the universal relation in A.
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Solution
A
=
{
2
,
3
,
5
,
7
,
10
}
R
1
=
{
(
2
,
2
)
,
(
3
,
3
)
,
(
5
,
5
)
,
(
7
,
7
)
,
(
10
,
10
)
}
R
2
=
A
×
A
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0
Similar questions
Q.
Let
R
1
,
R
2
are relation defined on
Z
such that
a
R
1
b
⟺
(
a
−
b
)
is divisible by
3
and
a
R
2
b
⟺
(
a
−
b
)
is divisible by
4
. Then which of the two relation
(
R
1
∪
R
2
)
,
(
R
1
∩
R
2
)
is an equivalence relation?
Q.
Show that the relation 'a R b' defined by
(
a
−
b
)
is an even integer, is an equivalence relation.
Q.
Let
R
1
be a relation from
A
=
{
1
,
3
,
5
,
7
}
to
B
=
{
2
,
4
,
6
,
8
}
and
R
2
be another relation from
B
to
C
=
{
1
,
2
,
3
,
4
}
as defined below:
(i) An element
x
in
A
is related to an element
y
in
B
(under
R
1
) if
x
+
y
is divisible by 3.
(ii) An element
x
in
B
is related to an element
y
in
C
(under
R
2
) if
x
+
y
is even but not divisible by 3.
Which is the composite relation
R
1
R
2
from
A
to
C
?
Q.
Show that the relation 'a R b if and only if
a
−
b
is an even integer defined on the Z of integers is an equivalence relation.
Q.
Let n be a fixed positive integer. Define a relation R on Z as follows:
(a, b) ∈ R ⇔ a − b is divisible by n.
Show that R is an equivalence relation on Z.
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