UnkleRhaukus
  • UnkleRhaukus
\[\begin{array}{ccccc}\phi & \neg \phi & \psi & \phi \Rightarrow \psi & \neg \phi \vee \psi \\ \hline \\T&F&T &T&?\\T&F&F&F&?\\F&T&T&T&?\\F&T&F&T&?\end{array}\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
RedPrince
  • RedPrince
T F T F
UnkleRhaukus
  • UnkleRhaukus
i think i made a mistake in the table already
UnkleRhaukus
  • UnkleRhaukus
sorry about that

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More answers

RedPrince
  • 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
  • RedPrince
post your question again and right!!
UnkleRhaukus
  • 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
  • UnkleRhaukus
it makes sense now, your answer form before , was right for the table i posted originally
RedPrince
  • 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
  • UnkleRhaukus
?
swissgirl
  • swissgirl
hmmm It seems to be that you are correct Unkle
swissgirl
  • swissgirl
me*
swissgirl
  • swissgirl
I cant seem to find where you went wrong. Everything seems correct
UnkleRhaukus
  • 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
  • swissgirl
The last column is obv false
swissgirl
  • swissgirl
I am not sure what that sign is of the second to last column
anonymous
  • anonymous
You were correct above, proving that the statements are logically equivalent
UnkleRhaukus
  • UnkleRhaukus
|dw:1348840677936:dw|
UnkleRhaukus
  • UnkleRhaukus
phi does not imply psi
swissgirl
  • swissgirl
hmmm Y have I never come across that one????? Ok Let me go get my book and see
swissgirl
  • swissgirl
Well isnt that then the same as ~(P->Q) I mean it should just be the opposite of the column before
UnkleRhaukus
  • 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
  • swissgirl
waitttt we didnt finish the previous one lol
UnkleRhaukus
  • UnkleRhaukus
is \[\phi\nRightarrow\psi\] the same as \[\neg\phi\Rightarrow\psi\]?
swissgirl
  • swissgirl
Noooo IN brackets
swissgirl
  • swissgirl
\(\neg(\phi\Rightarrow\psi)\)
UnkleRhaukus
  • UnkleRhaukus
hmm,
swissgirl
  • swissgirl
cuz idk I remember doing this stuff and we never came across that symbol
UnkleRhaukus
  • UnkleRhaukus
ok so you were right\[\phi\nRightarrow\psi\]\[\downarrow\]\[\neg(\phi\Rightarrow\psi)\]\[\downarrow\] opposite to the previous column,
swissgirl
  • swissgirl
yup
swissgirl
  • swissgirl
The last column is F T F F
UnkleRhaukus
  • 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
  • swissgirl
Ya that is correct
UnkleRhaukus
  • UnkleRhaukus
how did you get the last column ?
swissgirl
  • 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
  • UnkleRhaukus
i dont think i understand the difference between ¬φ ∨ ψ these φ ∨ ¬ψ
swissgirl
  • 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
  • swissgirl
FALSE OR FALSE=FALSE
swissgirl
  • swissgirl
The only difference is which column you will use.
swissgirl
  • swissgirl
Like one phi is negative and the other psi is negative
swissgirl
  • swissgirl
Well basically if you dont understand the difference then you are basically not following how truth tables are formed
swissgirl
  • swissgirl
ok lets make a truth table.
swissgirl
  • swissgirl
|dw:1348842795418:dw|
swissgirl
  • swissgirl
This drawing board was def testing my patience
swissgirl
  • 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
  • swissgirl
Do you follow?
UnkleRhaukus
  • UnkleRhaukus
YES that table makes sense now thankyou ! @swissgirl
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
  • 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
  • swissgirl
I dont like the second part of your conclusion Are you sure that it is correct?
UnkleRhaukus
  • UnkleRhaukus
oh yeah i got that a wrong
UnkleRhaukus
  • UnkleRhaukus
\[\phi\nRightarrow\psi\qquad\leftrightarrow\qquad\phi\wedge\neg\psi\]
swissgirl
  • swissgirl
YAAA thats correct
UnkleRhaukus
  • UnkleRhaukus
thanks again,

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