Logic equivalence and implication, question

[sadsadsadsa]

Hey guys I am having a bit of a difficult time with this question, if some one could help me out it would be appreciated, thanks.

Consider the following argument. "If the weather is fine, and the train is early, then the dog will sit on the tuckerbox. The train will be early, (but) also there will be rain. So the dog will not sit on the tuckerbox."Let W mean "the weather will be fine", E mean "the train will come early" and D mean "the dog will sit on the tuckerbox".

I get a formula like this: (W v E -> D) ^ (E ^ ~W) -> ~D. Am i right? I don't know how to do the rest. When i try working out the second question i get BDFH, i think I am right for that one but the first question I am still not sure.

(1) (2)
View attachment 4371View attachment 4372

 

[Evgeny.Makarov]

Does the "comparison table" mean "truth table"?

I get a formula like this: (W v E -> D) ^ (E ^ ~W) -> ~D. Am i right?

It should say $W\land E$, not $W\lor E$.

When i try working out the second question i get BDFH

Isn't it the answer to the first question, i.e., rows where D is T?

the first question I am still not sure.

Do you know how to construct truth tables? If yes, then what exactly is your difficulty? If no, then you should be asking for references describing how to do it.

You can construct a truth table using the mathematics software system SageMath if you go here, enter the following code:

import sage.logic.propcalc as propcalc
f = propcalc.formula("(W & E -> D) & (E & ~W) -> ~D")
f.truthtable()

and press "Evaluate".

 

[sadsadsadsa]

Does the "comparison table" mean "truth table"?

It should say $W\land E$, not $W\lor E$.

Isn't it the answer to the first question, i.e., rows where D is T?

Do you know how to construct truth tables? If yes, then what exactly is your difficulty? If no, then you should be asking for references describing how to do it.

You can construct a truth table using the mathematics software system SageMath if you go here, enter the following code:

import sage.logic.propcalc as propcalc
f = propcalc.formula("(W & E -> D) & (E & ~W) -> ~D")
f.truthtable()

and press "Evaluate".

This is wrong, i found the compound proposition equation for the first premisis, second premisis, and conclusion but somehow i keep getting the wrong answer. The second question which asked [TABLE="width: 100%"]
[TR]
[TD]In which rows of the last column does T appear?

the answer was B,D,F,H just like I said, but the first question is still not right.

[/TD]
[/TR]
[/TABLE]

 

[Evgeny.Makarov]

This is wrong, i found the compound proposition equation for the first premisis, second premisis, and conclusion but somehow i keep getting the wrong answer.

The first premise is, "If the weather is fine and the train is early, then the dog will sit on the tuckerbox". The formula should therefore be $W\land E\to D$, not $W\lor E\to D$. Do you agree?

The truth table for $(W\land E\to D)\land(E\land\neg W)\to\neg D$ has a single F in the last column, namely, for $E=D=T$ and $W=F$. It has T in all other rows. The formula $(W\lor E\to D)\land(E\land\neg W)\to\neg D$ has the same truth table. Which formula gives you T in rows 2, 4, 6, 8 (B, D, F, H)?

 

[sadsadsadsa]

The first premise is, "If the weather is fine and the train is early, then the dog will sit on the tuckerbox". The formula should therefore be $W\land E\to D$, not $W\lor E\to D$. Do you agree?

The truth table for $(W\land E\to D)\land(E\land\neg W)\to\neg D$ has a single F in the last column, namely, for $E=D=T$ and $W=F$. It has T in all other rows. The formula $(W\lor E\to D)\land(E\land\neg W)\to\neg D$ has the same truth table. Which formula gives you T in rows 2, 4, 6, 8 (B, D, F, H)?

I get the same formula as you, but i know for sure B,D,F,H is the answer for the second question and should be the last column, i do not know what formula gives this. what do you get for the second last column as the answer, because so far i keep getting it wrong.

Here is the whole question I just don't know that one question:

View attachment 4375

 

[Evgeny.Makarov]

In the standard truth table, the column for the last variable (D in this case) has T precisely in even rows when rows are counted from 1. You can see the complete truth table generated by Sage as described in post #2. Other than that, I don't understand how you are constructing your truth table and even whether "comparison table" is the same as "truth table"; you have not responded to my question about that.

 

[sadsadsadsa]

In the standard truth table, the column for the last variable (D in this case) has T precisely in even rows when rows are counted from 1. You can see the complete truth table generated by Sage as described in post #2. Other than that, I don't understand how you are constructing your truth table and even whether "comparison table" is the same as "truth table"; you have not responded to my question about that.

I constructed my truth table just like you suggested, all I cannot understand is what the answer is for the second last column. I don't understand isn't my comparison table just a truth table for my formula, what am i doing wrong? What do you get for the second last column because whatever I'm putting as my answer I am doing something wrong. CAN ANYONE HELP ME?

 

[Evgeny.Makarov]

The term "comparison table" is not standard in propositional logic. Perhaps it is important to figure out exactly what it means and what columns are last and second last (in general, not for this specific argument). Only you can do this by reviewing your textbook or lecture notes. If you find the definition, post it here and we will try to figure out the apparent answer to question 15 (B, D, F, H). So far all I can do it show the truth table for the formula that corresponds to this argument.

W      E      D      value
False  False  False  True   
False  False  True   True   
False  True   False  True   
False  True   True   False  
True   False  False  True   
True   False  True   True   
True   True   False  True   
True   True   True   True

It is also possible that question 15 is mistaken and is asking about the second last column after all.