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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”...

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Exercises 1–4 deal with these relations on the set of real numbers:

R1= {(a, b) ∈R2| a > b}, the “greater than” relation,

R2= {(a, b) ∈R2| a ≥ b}, the “greater than or equal to” relation,

R3= {(a, b) ∈R2| a < b}, the “less than” relation,

R4= {(a, b) ∈R2| a ≤ b}, the “less than or equal to” relation,

R5= {(a, b) ∈R2| a = b}, the “equal to” relation,

R6= {(a, b) ∈R2| a ≠ b}, the “unequal to” relation.

1. Find

a) R1∪R3.

b) R1∪R5.

c) R2∩ R4.

d) R3∩ R5.

e) R1− R2.

f) R2− R1.

g) R1⊕R3.

h) R2⊕R4.

2. Find

a) R2∪R4.

b) R3∪R6.

c) R3∩ R6.

d) R4∩ R6.

e) R3− R6.

f) R6− R3.

g) R2⊕R6.

h) R3⊕R5.

3. Find

a) R1? R1.

b) R1? R2.

c) R1? R3.

d) R1? R4.

e) R1? R5.

f) R1? R6.

g) R2? R3.

h) R3? R3.

4. Find

a) R2? R1.

b) R2? R2.

c) R3? R5.

d) R4? R1.

e) R5? R3.

f) R3? R6.

g) R4? R6.

h) R6? R6.

Answered Same Day Dec 29, 2021

Solution

Robert answered on Dec 29 2021
111 Votes
554593-7
Consider the sets
(
)
{
}
2
1
,
RabRa
=Î
(
)
{
}
2
2
,
RabRa
=γ
(
)
{
}
2
3
,
RabRa
=Î
(
)
{
}
2
4
,
RabRa
=Σ
(
)
{
}
2
5
,
RabRa
=Î=
(
)
{
}
2
6
,
RabRa
=ι
1.
(a)
The objective is to find
13
RR
È
(
)
{
}
(
)
{
}
(
)
{
}
22
13
2
6
,,
,
RRabRababRa
abRa
R
È=Î>ÈÎ
=ι
=
(b)
The objective is to find
15
RR
È
(
)
{
}
(
)
{
}
(
)
{
}
22
15
2
2
,,
,
RRabRababRa
abRa
R
È=Î>ÈÎ=
=γ
=
(c)
The objective is to find
24
RR
Ç
(
)
{
}
(
)
{
}
(
)
{
}
22
24
2
5
,,
,
RRabRababRa
abRa
R
Ç=γÇΣ
=Î=
=
(d)
The objective is to find
35
RR
Ç
(
)
{
}
(
)
{
}
22
35
,,
null set
RRabRababRa
Ç=Î<ÇÎ=
=Æ
=
(e)
The objective is to find
12
RR
-
(
)
{
}
(
)
{
}
22
12
,,
null set
RRabRababRa
-=Î>-γ
=Æ
=
(f)
The objective is to find
21
RR
-
(
)
{
}
(
)
{
}
(
)
{
}
22
21
2
5
,,
,
RRabRababRa
abRa
R
-=γ-Î
=Î=
=
(g)
The objective is to find
13
RR
Å
(
)
{
}
(
)
{
}
22
13
13
,,
RRabRababRa
RR
Å=Î>ÅÎ
=È
(h)
The objective is to find
24
RR
Å
(
)
{
}
(
)
{
}
22
24
24
,,
RRabRababRa
RR
Å=γÅΣ
=È
2.
(a)
The objective is to find
24
RR
È
(
)
{
}
(
)
{
}
(
)
{
}
22
24
2
6
,,
,
RRabRababRa
abRa
R
È=γÈΣ
=ι
=
(b)
The objective is to find
36
RR
È
(
)
{
}
(
)
{
}
(
)
{
}
22
36
2
6
,,
,
RRabRababRa
abRa
R
È=Î<Èι
=ι
=
(c)
The objective is to find
36
RR
Ç
(
)
{
}
(
)
{
}
(
)
{
}
22
36
2
3
,,
,
RRabRababRa
abRa
R
Ç=Î<Çι
=Î
=
(d)
The objective is to find
46
RR
Ç
(
)
{
}
(
)
{
}
(
)
{
}
22
46
2
3
,,
,
RRabRababRa
abRa
R
Ç=ΣÇι
=Î
=
(e)
The objective is to find...
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