anonymous
  • anonymous
Could someone please help me with this question? Anyone? :c Read the two statements shown below. If the weather is not cold, Meg will go swimming. The weather is cold, or Meg will go swimming. Create truth tables for the logical form of the two statements (not to be submitted). Use the truth tables to determine whether the two statements are logically equivalent. Justify your answer.
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@Hero pwease help...
anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
do you know how to create truth tables?

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More answers

anonymous
  • anonymous
Somewhat... Thats with all the odd symbols right?
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
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.
anonymous
  • anonymous
@jim_thompson5910 I have no idea what I'm doing sorry.
anonymous
  • anonymous
@Sujay But how to you justify that? Just by looking at it and logically processing it?
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
|dw:1355618482901:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1355618539480:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1355618570286:dw|
anonymous
  • anonymous
Could you explain what all that means? O _ O
jim_thompson5910
  • jim_thompson5910
so that's the truth table for ~p -> q which is the translation of "If the weather is not cold, Meg will go swimming."
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
|dw:1355618581504:dw|
jim_thompson5910
  • jim_thompson5910
then you fill out the ~P column by flipping everything you see in the P column
anonymous
  • anonymous
This is probably a stupid question but how come there are 4 in each column?
jim_thompson5910
  • jim_thompson5910
because there are 2^2 = 4 ways to have truth values for P and Q when they pair up
jim_thompson5910
  • jim_thompson5910
TT TF FT FF
anonymous
  • anonymous
OH!
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
TT TF FT FF
anonymous
  • anonymous
Hold on I kinda forgot the question
anonymous
  • anonymous
How do we figure out if its logically equilvalent? Do I just for whichever statement makes sense in that table?
jim_thompson5910
  • jim_thompson5910
make a truth table for the second statement "The weather is cold, or Meg will go swimming"
jim_thompson5910
  • jim_thompson5910
and compare the truth values in the last column
anonymous
  • anonymous
Ya Muzic, that is what I did--something I learned in Geometry.
anonymous
  • anonymous
???
anonymous
  • anonymous
how did you guys make that table? IS there like a tool or something?
jim_thompson5910
  • jim_thompson5910
I used the draw feature
jim_thompson5910
  • jim_thompson5910
under the text box is the draw button
anonymous
  • anonymous
Oh sorry I'm stupid -_-
anonymous
  • anonymous
Okay this is probably wrong but
jim_thompson5910
  • jim_thompson5910
no worries and you're not
anonymous
  • anonymous
|dw:1355619318974:dw|
anonymous
  • anonymous
... D:
jim_thompson5910
  • jim_thompson5910
I'll make a blank table for you to fill out
anonymous
  • anonymous
Oh I was just doing the last one like you said. do the other columns matter?
jim_thompson5910
  • jim_thompson5910
|dw:1355619401948:dw|
jim_thompson5910
  • jim_thompson5910
no not at the end, the other columns just build up to the last column
anonymous
  • anonymous
How do you fill these things out?
jim_thompson5910
  • jim_thompson5910
click on the pencil that's on my drawing
jim_thompson5910
  • jim_thompson5910
then you can edit what i did and add to it
anonymous
  • anonymous
I meant like the whole logical putting stuff together thing (t/f)...but okay!
jim_thompson5910
  • jim_thompson5910
oh you start off with T, T, F, F in column 1 then T, F, T, F in column 2
anonymous
  • anonymous
|dw:1355619574811:dw|
jim_thompson5910
  • jim_thompson5910
good, now fill out the last column
jim_thompson5910
  • jim_thompson5910
P v Q is only false when both P and Q are false
jim_thompson5910
  • jim_thompson5910
otherwise, P v Q is true
anonymous
  • anonymous
with what I came up before?
jim_thompson5910
  • jim_thompson5910
yeah add to what you just did
anonymous
  • anonymous
|dw:1355619650799:dw|
anonymous
  • anonymous
O_O
jim_thompson5910
  • jim_thompson5910
no, f is in the wrong spot
jim_thompson5910
  • jim_thompson5910
in the last column
anonymous
  • anonymous
omg confuse
anonymous
  • anonymous
Does it go as the first one?
jim_thompson5910
  • jim_thompson5910
no, it goes like this |dw:1355619731798:dw|
anonymous
  • anonymous
Why does it go down there?
jim_thompson5910
  • jim_thompson5910
since in the last row, both P and Q are false
jim_thompson5910
  • jim_thompson5910
because P v Q is only false when both P and Q are false
jim_thompson5910
  • jim_thompson5910
otherwise, P v Q is true
anonymous
  • anonymous
the columns are the same! :O
anonymous
  • anonymous
I mean the first and second statement's last columns