\[\begin{array}{ccccc}\phi & \neg \phi & \psi & \phi \Rightarrow \psi & \neg \phi \vee \psi \\ \hline \\T&F&T &T&?\\T&F&F&F&?\\F&T&T&T&?\\F&T&F&T&?\end{array}\]

- UnkleRhaukus

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- RedPrince

T
F
T
F

- UnkleRhaukus

i think i made a mistake in the table already

- UnkleRhaukus

sorry about that

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## More answers

- 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

- RedPrince

post your question again and right!!

- 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?

- UnkleRhaukus

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

- 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

- UnkleRhaukus

?

- swissgirl

hmmm It seems to be that you are correct Unkle

- swissgirl

me*

- swissgirl

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

- UnkleRhaukus

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

- swissgirl

The last column is obv false

- swissgirl

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

- anonymous

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

- UnkleRhaukus

|dw:1348840677936:dw|

- UnkleRhaukus

phi does not imply psi

- swissgirl

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

- swissgirl

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

- UnkleRhaukus

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

- swissgirl

waitttt we didnt finish the previous one lol

- UnkleRhaukus

is
\[\phi\nRightarrow\psi\]
the same as
\[\neg\phi\Rightarrow\psi\]?

- swissgirl

Noooo IN brackets

- swissgirl

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

- UnkleRhaukus

hmm,

- swissgirl

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

- UnkleRhaukus

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

- swissgirl

yup

- swissgirl

The last column is
F
T
F
F

- UnkleRhaukus

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

- swissgirl

Ya that is correct

- UnkleRhaukus

how did you get the last column ?

- 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

- UnkleRhaukus

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

- 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

- swissgirl

FALSE OR FALSE=FALSE

- swissgirl

The only difference is which column you will use.

- swissgirl

Like one phi is negative and the other psi is negative

- swissgirl

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

- swissgirl

ok lets make a truth table.

- swissgirl

|dw:1348842795418:dw|

- swissgirl

This drawing board was def testing my patience

- 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

- swissgirl

Do you follow?

- UnkleRhaukus

YES
that table makes sense now
thankyou !
@swissgirl

- 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

- UnkleRhaukus

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

- swissgirl

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

- UnkleRhaukus

oh yeah i got that a wrong

- UnkleRhaukus

\[\phi\nRightarrow\psi\qquad\leftrightarrow\qquad\phi\wedge\neg\psi\]

- swissgirl

YAAA thats correct

- UnkleRhaukus

thanks again,

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