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@Hero pwease help...
do you know how to create truth tables?
Somewhat... Thats with all the odd symbols right?
not sure what you mean by "Thats with all the odd symbols", but go ahead and make one and post it here so we can see it
No, because she can go swimming and the weather can be cold. The first statement only guarantees swimming if the weather isn't cold. It doesn't put away the possibility of her going swimming in cold weather.
@jim_thompson5910 I have no idea what I'm doing sorry.
@Sujay But how to you justify that? Just by looking at it and logically processing it?
ok I'll start you off let p: The weather is cold q: Meg will go swimming So start off |dw:1355618416718:dw|the truth table to get
Could you explain what all that means? O _ O
so that's the truth table for ~p -> q which is the translation of "If the weather is not cold, Meg will go swimming."
you start off with P and Q and you fill out the first column to be T, T, F, F then you do T, F, T, F for the second column this basically sets up all the possible truth value pairings for P and Q
then you fill out the ~P column by flipping everything you see in the P column
This is probably a stupid question but how come there are 4 in each column?
because there are 2^2 = 4 ways to have truth values for P and Q when they pair up
TT TF FT FF
finally, you fill out the ~P -> Q column by only writing F if ~P is true and Q is false otherwise, its true by default
TT TF FT FF
Hold on I kinda forgot the question
How do we figure out if its logically equilvalent? Do I just for whichever statement makes sense in that table?
make a truth table for the second statement "The weather is cold, or Meg will go swimming"
and compare the truth values in the last column
Ya Muzic, that is what I did--something I learned in Geometry.
how did you guys make that table? IS there like a tool or something?
I used the draw feature
under the text box is the draw button
Oh sorry I'm stupid -_-
Okay this is probably wrong but
no worries and you're not
I'll make a blank table for you to fill out
Oh I was just doing the last one like you said. do the other columns matter?
no not at the end, the other columns just build up to the last column
How do you fill these things out?
click on the pencil that's on my drawing
then you can edit what i did and add to it
I meant like the whole logical putting stuff together thing (t/f)...but okay!
oh you start off with T, T, F, F in column 1 then T, F, T, F in column 2
good, now fill out the last column
P v Q is only false when both P and Q are false
otherwise, P v Q is true
with what I came up before?
yeah add to what you just did
no, f is in the wrong spot
in the last column
Does it go as the first one?
no, it goes like this |dw:1355619731798:dw|
Why does it go down there?
since in the last row, both P and Q are false
because P v Q is only false when both P and Q are false
otherwise, P v Q is true
the columns are the same! :O
I mean the first and second statement's last columns
you are correct, so they are logically equivalent
MHMMM! So I just write they are logically equilvalent... how do I justify that in words
they produce the same last column in each truth table, so they are logically equivalent
Lol if I write that will my teacher say something about not explaining fully?
basically, you can plug in the same truth values for either ~P -> Q or P v Q and you'll get the same truth values for each possible input