Exercises 1–4 deal with these relations on the set of real numbers: R 1 = { (a, b) ∈R 2 | a > b } , the “greater than” relation, R 2 = { (a, b) ∈R 2 | a ≥ b } , the “greater than or equal to”...

554593-7
Consider the sets
(
)
{
}
2
1
,
RabRab
=Î>
(
)
{
}
2
2
,
RabRab
=γ
(
)
{
}
2
3
,
RabRab
=Î<
(
)
{
}
2
4
,
RabRab
=Σ
(
)
{
}
2
5
,
RabRab
=Î=
(
)
{
}
2
6
,
RabRab
=ι
1.
(a)
The objective is to find
13
RR
È
(
)
{
}
(
)
{
}
(
)
{
}
22
13
2
6
,,
,
RRabRababRab
abRab
R
È=Î>ÈÎ<
=ι
=
(b)
The objective is to find
15
RR
È
(
)
{
}
(
)
{
}
(
)
{
}
22
15
2
2
,,
,
RRabRababRab
abRab
R
È=Î>ÈÎ=
=γ
=
(c)
The objective is to find
24
RR
Ç
(
)
{
}
(
)
{
}
(
)
{
}
22
24
2
5
,,
,
RRabRababRab
abRab
R
Ç=γÇΣ
=Î=
=
(d)
The objective is to find
35
RR
Ç
(
)
{
}
(
)
{
}
22
35
,,
null set
RRabRababRab
Ç=Î<ÇÎ=
=Æ
=
(e)
The objective is to find
12
RR
-
(
)
{
}
(
)
{
}
22
12
,,
null set
RRabRababRab
-=Î>-γ
=Æ
=
(f)
The objective is to find
21
RR
-
(
)
{
}
(
)
{
}
(
)
{
}
22
21
2
5
,,
,
RRabRababRab
abRab
R
-=γ-Î>
=Î=
=
(g)
The objective is to find
13
RR
Å
(
)
{
}
(
)
{
}
22
13
13
,,
RRabRababRab
RR
Å=Î>ÅÎ<
=È
(h)
The objective is to find
24
RR
Å
(
)
{
}
(
)
{
}
22
24
24
,,
RRabRababRab
RR
Å=γÅΣ
=È
2.
(a)
The objective is to find
24
RR
È
(
)
{
}
(
)
{
}
(
)
{
}
22
24
2
6
,,
,
RRabRababRab
abRab
R
È=γÈΣ
=ι
=
(b)
The objective is to find
36
RR
È
(
)
{
}
(
)
{
}
(
)
{
}
22
36
2
6
,,
,
RRabRababRab
abRab
R
È=Î<Èι
=ι
=
(c)
The objective is to find
36
RR
Ç
(
)
{
}
(
)
{
}
(
)
{
}
22
36
2
3
,,
,
RRabRababRab
abRab
R
Ç=Î<Çι
=Î<
=
(d)
The objective is to find
46
RR
Ç
(
)
{
}
(
)
{
}
(
)
{
}
22
46
2
3
,,
,
RRabRababRab
abRab
R
Ç=ΣÇι
=Î<
=
(e)
The objective is to find...