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.

- anonymous

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- schrodinger

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- anonymous

@Hero pwease help...

- anonymous

@jim_thompson5910

- jim_thompson5910

do you know how to create truth tables?

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## More answers

- anonymous

Somewhat... Thats with all the odd symbols right?

- 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

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

@jim_thompson5910 I have no idea what I'm doing sorry.

- anonymous

@Sujay But how to you justify that? Just by looking at it and logically processing it?

- 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

|dw:1355618482901:dw|

- jim_thompson5910

|dw:1355618539480:dw|

- jim_thompson5910

|dw:1355618570286:dw|

- anonymous

Could you explain what all that means? O _ O

- 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

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

|dw:1355618581504:dw|

- jim_thompson5910

then you fill out the ~P column by flipping everything you see in the P column

- anonymous

This is probably a stupid question but how come there are 4 in each column?

- jim_thompson5910

because there are 2^2 = 4 ways to have truth values for P and Q when they pair up

- jim_thompson5910

TT
TF
FT
FF

- anonymous

OH!

- 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

TT
TF
FT
FF

- anonymous

Hold on I kinda forgot the question

- anonymous

How do we figure out if its logically equilvalent? Do I just for whichever statement makes sense in that table?

- jim_thompson5910

make a truth table for the second statement "The weather is cold, or Meg will go swimming"

- jim_thompson5910

and compare the truth values in the last column

- anonymous

Ya Muzic, that is what I did--something I learned in Geometry.

- anonymous

???

- anonymous

how did you guys make that table? IS there like a tool or something?

- jim_thompson5910

I used the draw feature

- jim_thompson5910

under the text box is the draw button

- anonymous

Oh sorry I'm stupid -_-

- anonymous

Okay this is probably wrong but

- jim_thompson5910

no worries and you're not

- anonymous

|dw:1355619318974:dw|

- anonymous

... D:

- jim_thompson5910

I'll make a blank table for you to fill out

- anonymous

Oh I was just doing the last one like you said. do the other columns matter?

- jim_thompson5910

|dw:1355619401948:dw|

- jim_thompson5910

no not at the end, the other columns just build up to the last column

- anonymous

How do you fill these things out?

- jim_thompson5910

click on the pencil that's on my drawing

- jim_thompson5910

then you can edit what i did and add to it

- anonymous

I meant like the whole logical putting stuff together thing (t/f)...but okay!

- jim_thompson5910

oh you start off with T, T, F, F in column 1
then T, F, T, F in column 2

- anonymous

|dw:1355619574811:dw|

- jim_thompson5910

good, now fill out the last column

- jim_thompson5910

P v Q is only false when both P and Q are false

- jim_thompson5910

otherwise, P v Q is true

- anonymous

with what I came up before?

- jim_thompson5910

yeah add to what you just did

- anonymous

|dw:1355619650799:dw|

- anonymous

O_O

- jim_thompson5910

no, f is in the wrong spot

- jim_thompson5910

in the last column

- anonymous

omg confuse

- anonymous

Does it go as the first one?

- jim_thompson5910

no, it goes like this
|dw:1355619731798:dw|

- anonymous

Why does it go down there?

- jim_thompson5910

since in the last row, both P and Q are false

- jim_thompson5910

because P v Q is only false when both P and Q are false

- jim_thompson5910

otherwise, P v Q is true

- anonymous