R 1 ( a , b ) in R 2 a b , the greater than relation, R 2 ( a , b ) in R 2 a b , the greater than or equal to relation, R 3 ( a , b ) in R 2 a b , the less than relation, R 4 ( a , b ) in R 2 a b , the less than or equal to relation, R 5 ( a , b ) in R 2 a b , the equal to relation, R 6 ( a , b ) in R 2 a b , the unequal to relation 3 4 Find a ) R 1 cup R 3 b ) R 1 cup R 5 c ) R 2 cap R 4 d ) R 3 cap R 5 e ) R 1 R 2 f ) R 2 R 1 g ) R 1 R 3 h ) R 2 R 4 3 5 Find a ) R 2 cup R 4 b ) R 3 cup R 6 c ) R 3 cap R 6 d ) R 4 cap R 6 e ) R 3 R 6 f ) R 6 R 3 g ) R 2 R 6 h ) R 3 R 5 3 6 Find a ) R 1 R 1 b ) R 1 R 2 c ) R 1 R 3 d ) R 1 R 4 e ) R 1 R 5 f ) R 1 R 6 g ) R 2 R 3 h ) R 3 R 3 3 7 Find a ) R 2 R 1 b ) R 2 R 2 c ) R 3 R 5 d ) R 4 R 1 e ) R 5 R 3 f ) R 3 R 6 g ) R 4 R 6 h ) R 6 R 6 3 8 Find the relations R 2 i for i 1 , 2 , 3 , 4 , 5 , 6 Find R 2 4 , R 2 5 , and R 2 6 where R 4 , R 5 and R 6 are as in exercises 3 4 3 8

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Question: R 1 = { ( a , b ) in R 2 a > b } , the greater than relation, R 2 = {

1 = {(

,

)

in R

2

>

},

the greater than relation,

2 = {(

,

)

in R

2

> =

},

the greater than or equal to relation,

3 = {(

,

)

in R

2

<

},

the less than relation,

4 = {(

,

)

in R

2

< =

},

the less than or equal to relation,

5 = {(

,

)

in R

2

=

},

the equal to relation,

6 = {(

,

)

in R

2

! =

},

the unequal to relation.

34 .

Find a

)

1 \

cup R

3 .

)

1 \

cup R

5 .

)

2 \

cap R

4 .

)

3 \

cap R

5 .

)

1

2 .

)

2

1 .

)

1

3 .

)

2

4 .

35 .

Find a

)

2 \

cup R

4 .

)

3 \

cup R

6 .

)

3 \

cap R

6 .

)

4 \

cap R

6 .

)

3

6 .

)

6

3 .

)

2

6 .

)

3

5 .

36 .

Find a

)

1

1 .

)

1

2 .

)

1

3 .

)

1

4 .

)

1

5 .

)

1

6 .

)

2

3 .

)

3

3 .

37 .

Find a

)

2

1 .

)

2

2 .

)

3

5 .

)

4

1 .

)

5

3 .

)

3

6 .

)

4

6 .

)

6

6 .

38 .

Find the relations R

2

i for i

= 1, 2, 3, 4, 5, 6

Find R

24,

25,

and R

26

where R

4,

5

and R

6

are as in exercises

34 - 38

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