Here's the question you clicked on:
UnkleRhaukus
\[\begin{array}{ccccc}\phi & \neg \phi & \psi & \phi \Rightarrow \psi & \neg \phi \vee \psi \\ \hline \\T&F&T &T&?\\T&F&F&F&?\\F&T&T&T&?\\F&T&F&T&?\end{array}\]
i think i made a mistake in the table already
¬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
post your question again and right!!
\[\begin{array}{ccccc}\phi & \neg \phi & \psi & \phi \Rightarrow \psi & \neg \phi \vee \psi \\ \hline \\T&F&T &T&T\\T&F&F&F&F\\F&T&T&T&T\\F&T&F&T&T\end{array}\] is that right?
it makes sense now, your answer form before , was right for the table i posted originally
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
hmmm It seems to be that you are correct Unkle
I cant seem to find where you went wrong. Everything seems correct
cool, what about this one \[\begin{array}{cccccc}\phi & \psi & \neg\psi & \phi \Rightarrow \psi & \phi \not\Rightarrow \psi &\psi\wedge\neg\psi\\ \hline \\T&T &F&T&\\T&F&T&F&\\F&T&F&T&\\F&F&T&T& \end{array}\]
The last column is obv false
I am not sure what that sign is of the second to last column
You were correct above, proving that the statements are logically equivalent
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phi does not imply psi
hmmm Y have I never come across that one????? Ok Let me go get my book and see
Well isnt that then the same as ~(P->Q) I mean it should just be the opposite of the column before
\[\begin{array}{cccccc}\phi & \psi & \neg\psi & \phi \Rightarrow \psi & \phi \nRightarrow \psi &\phi\wedge\neg\psi\\ \hline \\T&T &F&T&\\T&F&T&F&\\F&T&F&T&\\F&F&T&T& \end{array}\]
waitttt we didnt finish the previous one lol
is \[\phi\nRightarrow\psi\] the same as \[\neg\phi\Rightarrow\psi\]?
\(\neg(\phi\Rightarrow\psi)\)
cuz idk I remember doing this stuff and we never came across that symbol
ok so you were right\[\phi\nRightarrow\psi\]\[\downarrow\]\[\neg(\phi\Rightarrow\psi)\]\[\downarrow\] opposite to the previous column,
The last column is F T F F
\[\begin{array}{cccccc}\phi & \psi & \neg\psi & \phi \Rightarrow \psi & \phi \nRightarrow \psi &\phi\wedge\neg\psi\\ \hline \\T&T &F&T&F&F\\T&F&T&F&T&T\\F&T&F&T&F&F\\F&F&T&T&F&F \end{array}\]
how did you get the last column ?
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
i dont think i understand the difference between ¬φ ∨ ψ these φ ∨ ¬ψ
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
The only difference is which column you will use.
Like one phi is negative and the other psi is negative
Well basically if you dont understand the difference then you are basically not following how truth tables are formed
ok lets make a truth table.
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This drawing board was def testing my patience
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
YES that table makes sense now thankyou ! @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
i guess we can conclude that \[\phi\Rightarrow\psi\qquad\leftrightarrow\qquad\neg\phi\vee\psi\] and \[\phi\nRightarrow\psi\qquad\leftrightarrow\qquad\phi\vee\neg\psi\]
I dont like the second part of your conclusion Are you sure that it is correct?
oh yeah i got that a wrong
\[\phi\nRightarrow\psi\qquad\leftrightarrow\qquad\phi\wedge\neg\psi\]