UnkleRhaukus Group Title $\begin{array}{ccccc}\phi & \neg \phi & \psi & \phi \Rightarrow \psi & \neg \phi \vee \psi \\ \hline \\T&F&T &T&?\\T&F&F&F&?\\F&T&T&T&?\\F&T&F&T&?\end{array}$ one year ago one year ago

1. RedPrince Group Title

T F T F

2. UnkleRhaukus Group Title

3. UnkleRhaukus Group Title

4. RedPrince Group Title

¬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 Group Title

post your question again and right!!

6. UnkleRhaukus Group Title

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

7. UnkleRhaukus Group Title

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

8. RedPrince Group Title

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 Group Title

?

10. swissgirl Group Title

hmmm It seems to be that you are correct Unkle

11. swissgirl Group Title

me*

12. swissgirl Group Title

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

13. UnkleRhaukus Group Title

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 Group Title

The last column is obv false

15. swissgirl Group Title

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

16. satellite73 Group Title

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

17. UnkleRhaukus Group Title

|dw:1348840677936:dw|

18. UnkleRhaukus Group Title

phi does not imply psi

19. swissgirl Group Title

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

20. swissgirl Group Title

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

21. UnkleRhaukus Group Title

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

22. swissgirl Group Title

waitttt we didnt finish the previous one lol

23. UnkleRhaukus Group Title

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

24. swissgirl Group Title

Noooo IN brackets

25. swissgirl Group Title

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

26. UnkleRhaukus Group Title

hmm,

27. swissgirl Group Title

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

28. UnkleRhaukus Group Title

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

29. swissgirl Group Title

yup

30. swissgirl Group Title

The last column is F T F F

31. UnkleRhaukus Group Title

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

32. swissgirl Group Title

Ya that is correct

33. UnkleRhaukus Group Title

how did you get the last column ?

34. swissgirl Group Title

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 Group Title

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

36. swissgirl Group Title

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 Group Title

FALSE OR FALSE=FALSE

38. swissgirl Group Title

The only difference is which column you will use.

39. swissgirl Group Title

Like one phi is negative and the other psi is negative

40. swissgirl Group Title

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

41. swissgirl Group Title

ok lets make a truth table.

42. swissgirl Group Title

|dw:1348842795418:dw|

43. swissgirl Group Title

This drawing board was def testing my patience

44. swissgirl Group Title

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 Group Title

Do you follow?

46. UnkleRhaukus Group Title

YES that table makes sense now thankyou ! @swissgirl

47. swissgirl Group Title

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 Group Title

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 Group Title

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

50. UnkleRhaukus Group Title

oh yeah i got that a wrong

51. UnkleRhaukus Group Title

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

52. swissgirl Group Title

YAAA thats correct

53. UnkleRhaukus Group Title

thanks again,