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Mathematics
Problem
9. Show that each of the relation R in the set
A
=
{
x
∈
Z
:
0
≤
x
≤
12
}
\mathrm{A}=\{x \in \mathbf{Z}: 0 \leq x \leq 12\}
A
=
{
x
∈
Z
:
0
≤
x
≤
12
}
, given by (i)
R
=
{
(
a
,
b
)
:
∣
a
−
b
∣
\mathrm{R}=\{(a, b):|a-b|
R
=
{(
a
,
b
)
:
∣
a
−
b
∣
is a multiple of 4
}
\}
}
(ii)
R
=
{
(
a
,
b
)
:
a
=
b
}
\mathrm{R}=\{(a, b): a=b\}
R
=
{(
a
,
b
)
:
a
=
b
}
is an equivalence relation. Find the set of all elements related to 1 in each case.
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