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Byju's Answer
Standard XII
Mathematics
Transitive Relations
If a relation...
Question
If a relation R is defined on the set Z of integers as follows:
(a, b) ∈ R ⇔ a
2
+ b
2
= 25. Then, domain (R) is
(a) {3, 4, 5}
(b) {0, 3, 4, 5}
(c) {0, ± 3, ± 4, ± 5}
(d) none of these
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Solution
(c) {0, ± 3, ± 4, ± 5}
R
=
a
,
b
:
a
2
+
b
2
=
25
,
a
,
b
∈
Z
⇒
a
∈
-
5
,
-
4
,
-
3
,
-
2
,
-
1
,
0
,
1
,
2
,
3
,
4
,
5
and
b
∈
-
5
,
-
4
,
-
3
,
-
2
,
-
1
,
0
,
1
,
2
,
3
,
4
,
5
So
,
domain
(
R
)
=
0
,
±
3
,
±
4
,
±
5
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Similar questions
Q.
If a relation
R
is defined on the set of integers as follows:
(
a
,
b
)
∈
R
⇔
a
2
+
b
2
=
25
. Then domain of
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is
Q.
Write the domain of the relation R defined on the set Z of integers as follows:
(a, b) ∈ R ⇔ a
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Q.
A relation
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is defined on the set of integers as follows :
(
a
,
b
)
∈
R
⇔
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2
+
b
2
=
25.
Then domain of
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is
Q.
If R = {(x, y) : x, y ∈ Z, x
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Q.
The relation R defined on the set A = {1, 2, 3, 4, 5} by
R = {(a, b) : | a
2
− b
2
| < 16} is given by
(a) {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)}
(b) {(2, 2), (3, 2), (4, 2), (2, 4)}
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