Logic lecture for Thai student

7/23/2019 Logic lecture for Thai student

1/47

16 Jul 2015


2/47

................................................................................................................................................................................... 1

.................................................................................................................................................................... 2

................................................................................................................................................................... 8 ..................................................................................................................................................................................... 10 .......................................................................................................................................... 13 ............................................................................................................................................................................... 23 ....................................................................................................................................................................... 27 ........................................................................................................................................................................ 31 ......................................................................................................................................................... 35

......................................................................................................................................................... 41


3/47

1

3 > 5 3,674,196 .

> 5 ( 8 1)

, ,

76

1.

1. 2. 4 + 7 = 123. 4. 5. 4 6. 3

7.

8.

30


4/47

2

76

...... ...... ...... ...... ...... ...... ...... ...... ......

2 > 1 4 < 5 2 > 1 4 < 5

76 2+2 = 5 6 2+2 = 5

2 > 1 4 < 52 > 1 4 < 5

2+5 > 4 2+5 > 4

124 124 2+2 = 5 6

2 > 1 4 < 52 > 1 4 < 5 1

...... ...... () () ...... ...... 6

2

T T T

T F F

F T F

F F F

T T TT F T

F T T

F F F


5/47

3

2

...... ...... ( ) 2 > 1 4 < 5

2 > 1 4 < 5

2 < 9 6 + 8 = 14

2 > 1 4 < 52 > 1 4 < 5

not

2 3 2 3

~ 2 12 1 ~ ~

, , , , ~ 5T F .........

T T .........

F F .........

T T .........

F T ......... T T ......... ~F ......... T F .........T F ......... F T ......... T F ......... T T .........F F ......... ~T ......... F F ......... F F .........

~T (~F T) .........

, , ,

T T T

T F F

F T TF F T

T T T

T F FF T F

F F T

~T F

F T


6/47

4

, , ~

~ #

, , , , T F

F T

~ ~ ~

, , , ,

,

(

)

F ? T

T ? T ? T T

( ) #

~ ~ , ,

,

,

~ ~ ~

~

~ T T F F ~

~

~ T T F T F

F F

F

T

T

( )F

T

T

T

~ ~ F

T F

~ ~ F

T F? ? F F

T


7/47

5

~ T ~ ~

#

1. , ,

1. ~ ~ 2. ~ ~

3. ~ ~ 4. ~ ~ ~ ( )

2. 1. ~ ~ 2. ~

3. 4. ~ ~

~ ~ F

T FT T F F

F T


8/47

6

3. , , 1. ~ ~ 2. ( ) ~

3. ~~ ~ 4.

4. > 0 < >

=

[PAT 1 (.. 57)/2]1. ~ 2. ~ ~ ~ 3. ~ 4. ~

5.

, ,

[PAT 1 (.. 53)/1]1. 2. ~3. 4.


9/47

7

6. , ~ [PAT 1 (.. 54)/1]1. 2. ~

7. ,, ,

[PAT 1 (.. 57)/3]

1.

2.

~3. 4.


10/47

8

, , , ~

, ,

= 2

~ ~ ~ ~ 2 4

~ ~

~ ~ ~ ~ ~ ~ ~

T T T

T F F

F T FF F F

T T T

T F T

F T TF F F

T T T

T F F

F T TF F T

T T T

T F F

F T FF F T

~T FF T

~ ~ ~ ~ T TT F

F T

F F

1T

F

2 T T

T F

F TF F

3 T T T

T T F

T F TT F F

F T T

F T FF F T

F F F

4 T T T TT T T FT T F TT T F FT F T TT F T FT F F TT F F FF T T T

F T T FF T F TF T F F

F F T TF F T FF F F TF F F F


11/47

9

#

~ ~ ~ , , 3 8

#

1. ~

2. ~

~ ~ ~ ~ T T F F T

T F T T T

F T F F T

F F T F F

~ ~ ~ ~ ~ ~ ~ ~ ~T T T F F F F T T

T T F F F F T F F

T F T T T F F T T

T F F T T F T F TF T T F T T T F T

F T F F T T F T T

F F T T T T T F TF F F T T T F T T


12/47

10

= T

F

~ ~ ~

~ ~ ~

~ ~ ~ ~ ~ ~ #

~ ~ ~

~ ~ ~

~ ~ ~ ~ ~ ~ ( ) #

~

~

~ ~ #

~ ~ ~ ~ ~T T F F T T

T F F T T T

F T T F F F

F F T T T T

~ ~T T T T F F

T F T T F FF T F F T T

F F T F T T

~ ~ ~ ~ ~T T F F F F

T F F T F T

F T T F F T

F F T T T T


13/47

11

1.

2.

3. ~


14/47

12

4. , ,, , ,,

,, [PAT 1 (.. 57)/1]1. 2. ~3. ~ 4. ~ ~

,,T T T T

T T F TT F T F

T F F F

F T T T

F T F T

F F T T

F F F T


15/47

13

,, , ,

() 1.

2.

3.

4. ~~

1. ,

2. , ,

3.

4.

~ ~ ~ ~ ~ ~

~ ~ ~

***

~ ~ ~


16/47

14

1. T T F F

T T T T T ( ) TF F F F F

(

) F

2. T F T T T ( )

F F F ( ) 3. F T

~ F ~ F ~ ~ F ~ T ~ T ~ ~ T

( ) , , , ,

~ ~~ ~

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ ~ ~ ~ T ~ ~

( ) ( ) ~ (~ ) (~ ~ ) (~ ~ ) ~ ~ ( T ~ ) T ~ ~

~ ~~

~ ~

~ ~ ~

~ ~ ~ ~ ~

~ F ~~ F F

T T

T


17/47

15

/

~

#

~ ~()

~ #

~

~ ~ ~ ~ ~

#

~ ~ ~ ~ ~ ~

~ ~ ~ ~

~ ~ ~~ ~ ~~ ~~ ~ ~ ~

~( ~) ~ ~~~ ~

~


18/47

16

3 > 2 ~ 3 2 4 6 ~ 4 < 6 1


19/47

17

9. T 10.

11. 12. ~

13. 14. ~~ ~

15. ~ 16.

3. 1. ~ 2. ~ ~


20/47

18

3. 4.

5. 6.

7. 8. ~ ~

9.

10. > 0 > 0 > 0 0 0 0


21/47

19

11.

4. 1. ~ ~ 2. ~

3. ~ ~ ~ 4. ~~

5. 6. ~ ~ ~

7.

8. > <


22/47

20

9.

5. [PAT 1 (.. 53)/1]1. 2. ~ 3. 4. ~ ~ ~

6. , , [PAT 1 (.. 52)/1-2]1. 2.

7. ,, [PAT 1 (.. 52)/1]1. ( ) 2. ~ ~


23/47

21

8. , , [PAT 1 (.. 57)/3]1.

2.

9. , , ~ ~ ~

[PAT 1 (.. 55)/2]1. 2. 3. 4.

10. , , [A-NET 49/10]

1.

~

2.

~ ~ 3. ~ 4. ~~


24/47

22

11. , , ~ [PAT 1 (.. 54)/1]1. ~ ~ 2. q 3. ~ 4. ~

12.

, ~ [PAT 1 (.. 55)/3*]


25/47

23

~ ~

~ ~ F F ~ ~ #

1. 2. , ,

, , , ,

,

#

T T T TT F T T

F T T T

F F F T

~ ~ ~ ~ ~T T T F F F TT F F T T T T

F T F T F T T

F F F T T F F

F

T FT ?


26/47

24

~ , ,

, , , , ~ ~ #

2 TF F T

2 ,

TF TF

TF F T

F T ()

()

( ) #

F T

T

T, F

~ F

F FT F T F

T

F

? ?

F

T FT T

F

F T


27/47

25

:

~ ~

~ ~ ~ ~

~ ~

~ ~ #

#

1.

1. ~ 2.

3. (~) (~) 4. ~((() ) ~())

5. ~ 6. ()()

~ ~ ~ ~ ~ ~


28/47

26

7. ( )( ) 8. (()) (() )

9. ( ) ~( )

2. , [PAT 1 (.. 53)/1]1. ~ 2. 3. 4.

3. [PAT 1 (.. 55)/2]

1.

2.

~ ~ 3. ~ ~ 4. ~


29/47

27

1. 1.

2. 2.

2

-

(Conjunction)

(Simplification)

- ~ (Disjuctive Syllogism)

~ (Addition)

(Absorption)

(Modus Ponens)~ ~ (Modus Tollens) (Hypothetical Syllogism)

(Constructive Dilemma)

~ ~ ~ ~

1. ~ 2. 3. .........

1. 2. ~ 3. 4. 1 2 Modus Tollens ~ 2

~ 3 1


30/47

28

3 ~ 1 ~ 3 4 4 #

( ) ( )

1. 2. , ,

, , , ,

:

1. 2. 3. ~ ~

(3) ~ F

F (2) F F F (1) F F F F ~F F T #

( ... )F

T F

T T T T


31/47

29

1.

2.

1. 2. ~ ~

1. T 2. ~ T ~ F

(2) ~ F ~ T F T (1) F T F T #

1. ~ 2. 3. .........

1. 2. ~ 3. 4.

(1) ~ F F (2) F F F (3) F T F , T, F

1. ( ) 2. ~ ( ) 3. ( ) 4. ( , )

1, 2, 3 4 #


32/47

30

1.

1. 1. 2. 1. ~2. ~ ~ 2.

~

3. 1. 4. 1. 2. ~ 2. 3. ~ 3.

5. 1.

2.

6. 1. 2. 3.

2. [A-NET 51/1-1]1.

2.

1) ~ ~ 2) 3) ~


33/47

31

2 2+ 3 > 5 , 0 , 2

2 3 > 5 , 0 2 3 > 5 = 0 3 > 5

0

0

2 3 > 5 , 0 2 3 > 5 = 10 23 > 5

0 = 1 1 0 = 1

()

, , [ ]

[ ] 2 3 > 5 , 0

2 3 > 5 0

()


34/47

32

U U U U= {1, 2 ,3, 4}

4 0 = 1, 2, 3, 4 ( 5 U) 1 > 0 = 1 4 > 0 = 1, 2, 3, 4 > 0 = 1

U ( = ) 1,2,3,44 0 = 1, 2, 3, 4

N 1 > 0

(N) 1 0 1,1> 1 1 1= 1 >12 3 = 2 = 0.5

( )

( , , , )

> 1 > 0

> 1 > 0

T F >1 > 0 T F > 1 > 0 #

R 0 < 0 (R)

= 3 R

0

< 0 #

= 3 3 > 1 3 > 0 F F T= 0 0 > 1 0 > 0 F F T= 0.5 0.5 > 1 0.5 > 0 F T T= 2 2 > 1 2 > 0 T T T

= 3 3 0 3 < 0 F F T


35/47

33

0 < 0 2

0 < 0 0 = 1< 0

0 < 0 T F F #

1.

1. > 0 U= {1, 2, 3, 4} 2.

3. 2 = 0 U= {1, 0, 1} 4. I > 2

5. N2 1 6. I 1 = 0

7. 0 = 0 8. 0 = 0

9. 0 = 0 10. 0 = 0

11.


36/47

34

2. 1 = 1 1 > 2

[PAT 1 (.. 53)/2]1. ~ ~ 2. 3. 4.

3. ~ [PAT 1 (.. 54)/2]1. 2. ~ ~3. ~ 4. ~

4. [A-NET 50/1-3]1. 2. 3.

4.

~ 1. 2. 3. 4.


37/47

35

< 5 ,

0 ,

> 1

, , , , ,

4 ,

,

,

(

)

, ( )

U= {1, 0, 1} 1. 0 2. 03. 0 4. 0

1.

0

= 1, = 1 1 10 0

2. 0 = 0 , = 1 0 + 1 0 0

3.

= 1 0 4.

0 #

1 +

1

0

1 + 0 01 + 1 0

1 + 1 00 + 0 01 + 0 0


38/47

36

0

0

0

#

U=I 0

0 0 #

2 0

= 1 = 2

= 5 = 10 = 0.2 = 0.4

2 0 #

>

... ... 2 F ? ? T

>

> = 0 = 1 0 1 . F ? T= 3 = 4 3 4 . F ? T

=2 = 1 2 1 . F ? T


39/47

37

F ? > > #

1.

1. = 0 2. = 0

3. = 0 4. = 0

5. < 6. =

7. > 8. =

9. 10.

11. 12.

13. 14. <

15. 0 16. > 0

17. < 5 18. 0

19. 3 4 =

2. = {2, 1, 0, 1, 2} 1. > | | 3 2. = ||=||


40/47

38

3. = |||| 4. = 0 = 0

3. 1. > > 2. > 1

3. = 1 = 1 4. ||=||

4. {1, 0, 1} [PAT 1 (.. 53)/2]1. 2 > 0 2. 0 3. = 1 4. > 1

5. ={3, 2, 1, 1, 2, 3}[A-NET 49/1-9]

1. < 2. < 3. = 4. =


41/47

39

6. { | 0 < < 1 } [PAT 1 (.. 57)/2]1. [ < ] 2.

[

| | 3. 4. 9

9. = {1, 2, 1, 3, 2, 3} [PAT 1 (.. 52)/2]

1.

2.

= 3. 4.


43/47

41

(~) ( ) ~ ~ ~ ~

~, ~, ~, ~, ~, ~, ~, ~,

> 0 1 0 ~ > 0 1 0 ~ > 0 1 0

0 1 > 0 #

> 2 0 ~ > 2 0 ~~ > 2 0

> 2 ~ 0 > 2 > 0 #

~ [~( )]

[~(~ )] ~

~

#

1. 1. ||= 0 2.


44/47

42

3. 1 > 0 0 4. 1

5. 6.

7. 8.

2. ~ [PAT 1 (.. 52)/1]1.

~

2.

~

3. 4. ~


45/47

43

3. [A-NET 50/1-2]1. 1 = 2. [ ] ~ ~

4. [PAT 1 (.. 53)/2*]1. {1, 0, 1} = 2. > 0 0 < 0

< 0 0 > 03. > 0

0 <


46/47

44

1. 2, 4, 5, 6, 8

1. 1. T 2. T 3. T 4. F2. 1. T 2. F 3. T 4. T3. 1. T , F , F 2. T , F , F

3. T , T , F 4. T , F4. 3 5. 2 6. - 7. 1

1.

2.

1. 2. 3. 4. 3

1. 1. 2. ~ 3. ~ ~ 4. 5. ~ 6. 7. 8. 9. T 10 F 11. T12. 13. F

2. 1. ~ ~ 2. ~ ~ 3. ~ 4. ~ ~ 5. ~ ~ 6. T 7. 8. T9. ~ 10. T 11. ~ 12. 13. T 14. ~ ~ 15. ~ 16.

3.

1, 2, 4, 5, 7, 8, 9, 11

~ ~ T T F T

T F F T

F T T T

F F T F

~ ~ ~ T T T F F FT F F F T F

F T F T T F

F F T T F F


47/47

45

4. 2, 3, 6, 7, 95. 4 6. 1, 2 7. 1 8. 1, 29. 3 10. 4 11. 3 12. T

1. 1, 2, 5, 8 2. 3 3. 3

1. 1, 2, 4, 6 2. 2

1. 1, 2, 3, 4, 5, 7, 10, 11 2. 2 3. 14. 2

1. 2, 4, 6, 7, 11, 12, 14, 15, 17, 18 2. 1, 2 3. 24. 3 5. 3 6. 2 7. 48. 4 9. 1

1. 1. || 0 2. = 3. 1 0 > 0 4. 1 5. 6. 7. 8.

2. 2 3. 2 4. 2

Tunyaluck Martjutasaeranee

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Logic lecture for Thai student