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Mathematics
Mathematics
Problem
Let
A
=
{
1
,
2
,
3
}
=
B
A=\{1,2,3\}=B
A
=
{
1
,
2
,
3
}
=
B
and define the relation
S
=
{
(
x
,
y
)
∈
A
×
B
∣
y
≥
x
}
S=\{(x,y)\in A\times B\mid y\ge x\}
S
=
{(
x
,
y
)
∈
A
×
B
∣
y
≥
x
}
. For
k
∈
{
1
,
2
,
3
}
k\in\{1,2,3\}
k
∈
{
1
,
2
,
3
}
, consider the relation
R
k
=
{
(
1
,
1
)
,
(
2
,
k
)
,
(
3
,
3
)
}
.
R_k=\{(1,1),(2,k),(3,3)\}.
R
k
=
{(
1
,
1
)
,
(
2
,
k
)
,
(
3
,
3
)}
.
For which value(s) of
k
k
k
is
R
k
R_k
R
k
a subrelation of
S
S
S
? a)
k
=
1
k=1
k
=
1
b)
k
=
2
or
k
=
3
k=2 \text{ or } k=3
k
=
2
or
k
=
3
c)
k
=
3
k=3
k
=
3
d)
k
=
2
k=2
k
=
2
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