สารบัญ - RATH · PDF fileเซต 1 ความหมายของเซต เซต คือ กลุ่มของอะไรบางอย่าง เช่น

4 Mar 2018

.................................................................................................................................................................. 1 ................................................................................................................................................................ 3 ......................................................................................................................................................................... 5 / ............................................................................................................................................ 7 ....................................................................................................................................................................................... 8 ...................................................................................................................................................................... 11 - .................................................................................................................................................... 11 ........................................................................................................................................................... 13 .................................................................................................................................................... 20 ........................................................................................................................................................................... 23 ........................................................................................................................................................................ 28 ..................................................................................................................................... 33

1
N ( ) I R I+ ( N) R+ I R
2 1.
2. 6
6 : 1, 2, 3, 4, 5 : 5
1 2 3 4 5
500 : : 0
: , , , : 4
7 : 7, 14, 21, :
7 14 21
100 : 1, 2, 3, , 99 : 99
1 2 3 99
{ , , , }
( )
()
{ N | < 6 }

2
{, , , } { | }
6 {1, 2, 3, 4, 5} { | 6} { N | < 6}
100 {1, 2, 3, , 99} { I | > 100}
7 {7, 14, 21, } { | 7 } { R+ | 7 }
500 { } { | 500 }
: { }
1. 1. { | 10} 2. { I | 2 = 16}
3. { | 3 + 5 = 16} 4. { I | 5}
5. { N | 50} 6. { I | || 2}
7. { I+ | 0 } 8. { R | = 8}

3
(, , , , )
{ {, , } , {, } , {, , , } }
{ {1, 2} , {3, 4} , {5, 6} } 3 { {1} , {1, 2} , {1, 2, 3} } 3 { {1, 2, 3, 4} } 1 { {1, 2, 3, 4, } } 1 { { } } 1 { 1, 2 , {3, 4} } 3 { 1, {1} , {1, {1}} } 3 { 1, {{2, 3} , {{4}}} } 2
1. 1. { , {1} , {2} , {3} } 2. { {1, 2} , {3} }
3. { {1 , 2 , {3}} } 4. { 1, {1, 2} , {1, 2, 3} }
: , , : 3
: , : 2
: , , , : 4
: , , : 3

4
5. { { { } } } 6. { {1, } , }
7. { {1 , {2}} , {3, {}} } 8. { {{1}, {1, 2} , {1, {2}, 3}} }

5
, , , , , , , 1 {1, 2, 3} 17 {1, 2, 3, , 100} 1.2 R+ 3 { | } 1 {2, 3, 4} 17 {1, 2, 3, , 10} 1.2 N 9 { | 5 }
{ {1}, {2}, {3} } 3 {1} , {2} , {3} {1} { {1}, {2}, {3} } {2} { {1}, {2}, {3} } {3} { {1}, {2}, {3} } 1 { {1}, {2}, {3} } {{2}} { {1}, {2}, {3} }
{ {1, 2}, {2, 3} } 2 {1, 2} {2, 3} {1, 2} { {1, 2}, {2, 3} } {2, 3} { {1, 2}, {2, 3} } {1} { {1, 2}, {2, 3} } {1, 3} { {1, 2}, {2, 3} }
{ {1}, {2, 3}, { 1, {2, 3, {4}} } } 3 {1} , {2, 3} , {1, {2, 3, {4}}} {1} { {1}, {2, 3}, { 1, {2, 3, {4}} } } {2, 3} { {1}, {2, 3}, { 1, {2, 3, {4}} } } {1, {2, 3, {4}}} { {1}, {2, 3}, { 1, {2, 3, {4}} } } {2, 3, {4}} { {1}, {2, 3}, { 1, {2, 3, {4}} } }
() || ( {1, 5, 8} ) = 3 ( { I+ | < 8} ) = 7 ( { } ) = 0 ( {1, 2, 3, } ) = ( {8, 8, 8} ) = 1 ( {1, 5, 8, 8, 1, 8} ) = 3 ( { {1}, {2}, {3} } ) = 3 ( { {1, 2} , {2, 3} } ) = 2 ( { 1, {1}, {{1}} } ) = 3 ( { 1 , {2, {3}} } ) = 2
(= 0)

6
1. 1. 5 {25, 125} 2. 0 { } 3. 14 { N | 7 } 4. {1} { 1, {1, 2}, {{1}} } 5. 3 3 6. { } { } 7. { } { { } } 8. {1} { {1} , {2} } 9. {1, 2} { {1} , {2} } 10. {1, 2, 3, 4} { {1, 2}, {2, 3, 4} } 11. {2, 3} { 1, {1, 2}, {1, {2, 3}} } 12.
2. 1. ({ 3, 8, 9 }) = 2. ({ | = 4}) = 3. ({ I | 3 + 2 = 3}) = 4. () = 5. ({ }) = 6. ({ { } }) = 7. ({ {1, 3} , {1} , {3} }) = 8. ({ {1, {2}, {1, 2, {2}}, {1}} }) =
3. 1. {1, 2, 3, , 99999999} 2. { | 3 + 1 = 0} 3. N 4. { | 1 5} 5. 6. { {1, 2, 3, } }
4. . 1 . 1
. 2 [PAT 1 (.. 52)/1-21] 1. 1
2 2. 1
8 3. 1
16 4. 1
32

7
/ {1, 2, 3} = {1, 2, 3} {3, 5, 7, 9} = {5, 9, 3, 7} {1, 1, 2, 2, 1, 3} = {3, 2, 1, 2, 1} = {1, 2, 3} { | 3 5 = 16} = { N | 2 = 49} { {1, 2}, {2, 3} } = { {3, 2}, {2, 1} } {1, 2, 3, 4} {2, 3, 4, 5} {0} {1} { {1} } { 1 , {1, {2}} } { {2, {1}} , 1 }
: {1, 2, 3} {, , } {1, 5, 6, 8, 9} {, , , , } { | 2 = 1} {10, 11} { 1, {1, 2, 3} } { {1}, {2} } {1, 2, 3} { {1, 2}, 3 } {0}
:
1.
1. {1, 2, 2, 3} = {3, 2, 1} 2. { { }, {1, 2} } = { {2, 1}, } 3. { {1, 2}, {2, 3} } {3, 2, 1} 4. { { } } { } 5. 6.

8
{1, 2} {1, 2, 3} {1, 3, 5} {1, 2, 3, 4, 5} {5} {1, 3, 5} {1, 2, 3, 4} {1, 2, 3, 4} { N | 4} { N | 1} I+ R {0, 1} {1, 2, 3, 4} I I+ { | 2 = 4} {1, 2, 3, 4}
( ) {1, 2, 3} { {1}, {2, 3} } I
= {1, 2} , {1} {2} {1, 2}
{1} {1, 2, 3} {1} {1, 2, 3} {1, 2, 3} {1, 2, 3} {1, 2, 3} {1, 2, 3}
{1, {2}, {1, 2}} {1, 2, {1}, {2}, {1, 2}} {1, {2}, {1, 2}} 3 1 {2} {1, 2}
{1, 2, {1}, {2}, {1, 2}} 5 1 2 {1} {2} {1, 2}
{1, {2}, {1, 2}} {1, 2, {1}, {2}, {1, 2}} #
<
{1, {2}, {1, 2}} {1, 2, {1}, {2}, {1, 2}}
1 {2}
{1, 2}
1 2
{1} {2}
{1, 2}

9
{{1}, {2}} {{1}, {1, 2}, {1, {2}}} {{1}, {2}} 2 {1} {2}
{{1}, {1, 2}, {1, {2}}} 3 {1} {1, 2} {1, {2}}
{2}
{{1}, {2}} {{1}, {1, 2}, {1, {2}}} #
() ()
{1, {2}} {{1}, {1, 2}, {1, {2}}}
{1, {2}}
{1, {2}} {{1}, {1, 2}, {1, {2}}} #
1 {1, 2, 3} {1} {1, 2, 3} {1} {1, 2, 3} {1} { {1}, {2}, {3} } {1, 2, 3} { {3, 2, 1} } 1 {1, 2, 3} {2, 3} {1, 2, 3} {2, 3} { {1, 2}, {2, 3} } {2, 3} { {2}, {3}, {1, 2, 3} } {2, 3} { {2}, {3}, {1, 2, 3} } {1, 2, 3} {1, 2, 3}
1. = { N | 5} 1. 2. {1} 3. {2} 4. {3}
2. = { I | < 5} 1. 2. { I | < 4} 3. { N | < 5} 4. { N | > 0}
3. 1. 1 {1, 2, 3} 2. { { } }
3. { { } } 4. {1, 2} { {1}, {2, 1} }
{{1}, {2}} {{1}, {1, 2}, {1, {2}}}
{1} {2}
{1} {1, 2}
{1, {2}} ?
{1, {2}} {{1}, {1, 2}, {1, {2}}}
{1, {2}} {1} {1, 2} {1, {2}}

10
5. 0 6. 0
7. {1, 2, 3} 8. {1, 2, 3, } N
9. I N 10. {1, 2, 3, } {1, 2, 3}
11. 1 {1} 12. 1 {1}
13. {1} 1 14. {1} 1
15. {1, {1}} { 1, {1}, {1, {1}} } 16. {1, {1}} { 1, {1}, {1, {1}} }
17. {2, {3}} {{{3}, 2}, 2} 18. {{2, {3}}, {{1}}} {{2, {3}, {1}}, {{1}}}
19. 20. =
4. [O-NET 52/10] 1. 2. 3. 4.
5. = {1, 2, {1, 2}, {1, 2, 3}} [PAT 1 (.. 52)/4] 1. {1, 2} 2. {1, 2, 3} 3. {1, 2} 4. {1, 2, 3}
6. = {, 1, {1}} [PAT 1 (.. 52)/3] 1. 2. {}
3. {1, {1}} 4. {{1}, {1, {1}}}

11
= {1, 2, 3, , 10} = { | > 7} 7 ( 8, 9, 10, 11, 12, )
= {1, 2, 3, , 10} 1, 2, 3, , 10 11, 12, 13, U = {8, 9, 10} #
-
= {1, 2, 3, , 10} = {2, 3, 6} = {1, 3, 6, 8}
36
2 18
4, 5, 7, 9, 10
U
= {1, 2, 3, , 10} = {1, 3, 6, 7, 8} = {3, 6, 7}
U
3, 6, 7
18
2, 4,
5, 9, 10
= {1, 2, 3, , 10} = {1, 2, 3, 4} = {2, 4, 5, 6} C = {3, 4, 6, 7}
1
2
3 4 5
6 7
8, 9, 10
U
= {1, 2, 3, , 10} = {3, 8, 9} = {1, 5, 6, 10}
2, 4, 7
U 3, 8,
9 1, 5, 6, 10
2, 4, 5, 6, 8, 9, 10
= {1, 2, 3, , 10} = {1, 3, 7}
U 1, 3,
7

12
1. - 1. = {1, 2, 3, , 10} 2. = {1, 2, 3} = {1, 3, 5, 7} = {1} = {2, 4, 6, 8} = {1, 2}
3. = {1, 2, 3, 4, 5, 6} 4. = {1, 2, 3, 4} = {1, 2, 3} = {1, 2, 3} = {2, 3, 4} = {1, 4} = {1, 4} = {1, 3, 4}

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สารบัญ - RATH · PDF fileเซต 1 ความหมายของเซต เซต คือ กลุ่มของอะไรบางอย่าง เช่น