UnkleRhaukus 3 years ago $\begin{array}{ccccc}\phi & \neg \phi & \psi & \phi \Rightarrow \psi & \neg \phi \vee \psi \\ \hline \\T&F&T &T&?\\T&F&F&F&?\\F&T&T&T&?\\F&T&F&T&?\end{array}$

1. RedPrince

T F T F

2. UnkleRhaukus

3. UnkleRhaukus

4. RedPrince

¬ϕ∨ψ means if either ¬ϕ is true or either ψ is true or both are true then the answer is true otherwise it is false ¬ϕ is false but ψ is true so the answer is true, and so on

5. RedPrince

post your question again and right!!

6. UnkleRhaukus

$\begin{array}{ccccc}\phi & \neg \phi & \psi & \phi \Rightarrow \psi & \neg \phi \vee \psi \\ \hline \\T&F&T &T&T\\T&F&F&F&F\\F&T&T&T&T\\F&T&F&T&T\end{array}$ is that right?

7. UnkleRhaukus

it makes sense now, your answer form before , was right for the table i posted originally

8. RedPrince

last one is wrong one of ψ and ¬ϕ is true, so how can it be true.....!!! check this! http://www.hermit.cc/teach/ho/dbms/optable.htm

9. UnkleRhaukus

?

10. swissgirl

hmmm It seems to be that you are correct Unkle

11. swissgirl

me*

12. swissgirl

I cant seem to find where you went wrong. Everything seems correct

13. UnkleRhaukus

cool, what about this one $\begin{array}{cccccc}\phi & \psi & \neg\psi & \phi \Rightarrow \psi & \phi \not\Rightarrow \psi &\psi\wedge\neg\psi\\ \hline \\T&T &F&T&\\T&F&T&F&\\F&T&F&T&\\F&F&T&T& \end{array}$

14. swissgirl

The last column is obv false

15. swissgirl

I am not sure what that sign is of the second to last column

16. satellite73

You were correct above, proving that the statements are logically equivalent

17. UnkleRhaukus

|dw:1348840677936:dw|

18. UnkleRhaukus

phi does not imply psi

19. swissgirl

hmmm Y have I never come across that one????? Ok Let me go get my book and see

20. swissgirl

Well isnt that then the same as ~(P->Q) I mean it should just be the opposite of the column before

21. UnkleRhaukus

$\begin{array}{cccccc}\phi & \psi & \neg\psi & \phi \Rightarrow \psi & \phi \nRightarrow \psi &\phi\wedge\neg\psi\\ \hline \\T&T &F&T&\\T&F&T&F&\\F&T&F&T&\\F&F&T&T& \end{array}$

22. swissgirl

waitttt we didnt finish the previous one lol

23. UnkleRhaukus

is $\phi\nRightarrow\psi$ the same as $\neg\phi\Rightarrow\psi$?

24. swissgirl

Noooo IN brackets

25. swissgirl

$$\neg(\phi\Rightarrow\psi)$$

26. UnkleRhaukus

hmm,

27. swissgirl

cuz idk I remember doing this stuff and we never came across that symbol

28. UnkleRhaukus

ok so you were right$\phi\nRightarrow\psi$$\downarrow$$\neg(\phi\Rightarrow\psi)$$\downarrow$ opposite to the previous column,

29. swissgirl

yup

30. swissgirl

The last column is F T F F

31. UnkleRhaukus

$\begin{array}{cccccc}\phi & \psi & \neg\psi & \phi \Rightarrow \psi & \phi \nRightarrow \psi &\phi\wedge\neg\psi\\ \hline \\T&T &F&T&F&F\\T&F&T&F&T&T\\F&T&F&T&F&F\\F&F&T&T&F&F \end{array}$

32. swissgirl

Ya that is correct

33. UnkleRhaukus

how did you get the last column ?

34. swissgirl

Ok well that is known as the and connective And the rule there is that a true with False=False A false with a fasle is false and a true with a true =true And it should make sense logically in your brain FALSE AND FALSE=FALSE TRUE AND FALSE cant be true it must be FALSE TRUE AND TRUE is obv TRUE

35. UnkleRhaukus

i dont think i understand the difference between ¬φ ∨ ψ these φ ∨ ¬ψ

36. swissgirl

Ok well firstly the connective is the or connective and its always true except when both compartments are false So TRUE OR TRUE=TRUE TRUE OR FALSE=TRUE Lets take the sentence I went to bed early or i went to bed on time Its true statement even though one half of the sentence contradicts the other FALSE OR FALSE+FALSE

37. swissgirl

FALSE OR FALSE=FALSE

38. swissgirl

The only difference is which column you will use.

39. swissgirl

Like one phi is negative and the other psi is negative

40. swissgirl

Well basically if you dont understand the difference then you are basically not following how truth tables are formed

41. swissgirl

ok lets make a truth table.

42. swissgirl

|dw:1348842795418:dw|

43. swissgirl

This drawing board was def testing my patience

44. swissgirl

the way i figured out the last 2 columns was look at the appropriate 2 columns and decide if it would be true or false

45. swissgirl

Do you follow?

46. UnkleRhaukus

YES that table makes sense now thankyou ! @swissgirl

47. swissgirl

lol I hope so. Its kinda hard to explain but if you start from the wayyyyyy begginning then like once you get it its simple

48. UnkleRhaukus

i guess we can conclude that $\phi\Rightarrow\psi\qquad\leftrightarrow\qquad\neg\phi\vee\psi$ and $\phi\nRightarrow\psi\qquad\leftrightarrow\qquad\phi\vee\neg\psi$

49. swissgirl

I dont like the second part of your conclusion Are you sure that it is correct?

50. UnkleRhaukus

oh yeah i got that a wrong

51. UnkleRhaukus

$\phi\nRightarrow\psi\qquad\leftrightarrow\qquad\phi\wedge\neg\psi$

52. swissgirl

YAAA thats correct

53. UnkleRhaukus

thanks again,