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Urgent Help Required (2 Problems)

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Folks, I have no idea how to solve these two matters.

1. I need to show by the sentence tablueau method that the sentence [A V -A] is a logical consequence of any sentence "R."
And

2. I need to figure out what this binary truth-functional sentential connective (#) actually is in light of
P#P being a tautology, and Q#P not being a tautological consequence of the sentences P#Q and P.

This is homework, and I don't want people to think I'm just hunting for answers. I really don't know how to go about solving these.
Any tips for the process? Very grateful for any help...

@Horace phil,

I have to ask,what is the propositional logic system you are using? SD logic has many different versions of the same thing, so you may want to state the system that you are using. For instance, past members have mentioned what system they do under the author of the book they studied from. So for example, I know Herrick, Bergmann, etc, and as a result you know the particular inference, replacements, symbols, etc. What exactly is the make and edition of your SD/propositional logic?

I have seen a few of your posts which no one really answers, so it may help to explain which framework you are working under so that we become acquainted with your system. Logic is much like different dialects of the same language.

@VideCorSpoon,

Hello. I don't know. I can find out though.
Which parts of the question could mean something different if it was a different system I am using?
I don't even know where to start with these two questions...

@Horace phil,

Horace;76732 wrote:

Hello. I don't know. I can find out though.
Which parts of the question could mean something different if it was a different system I am using?
I don't even know where to start with these two questions...

What text are you using?

@Horace phil,

why is logic so complicated? isnt it just supposed to be the way the healthy brain works? are there actually different kinds of logic or is it that there are different kinds of logical proofs to show that we are being logical? the only thing i ever saw in the way of a book on logic was something called wff and pruf or something like that, and i didnt get it at all.

@Horace phil,

Horace;76721 wrote:

Folks

I'm on a campaign to reduce the use of the word "folks".

Horace;76721 wrote:

1. I need to show by the sentence tablueau method that the sentence [A V -A] is a logical consequence of any sentence "R."

Check the rules for your tree proof system. Many such systems allow insertion of a LEM branch (such as A v ~A) anywhere.

Horace;76721 wrote:

2. I need to figure out what this binary truth-functional sentential connective (#) actually is in light of
P#P being a tautology, and Q#P not being a tautological consequence of the sentences P#Q and P.

Well, there are four binary connectives. Try each one in place of "#" until you find a connective that allows all of the above to be true and consistent.

Horace;76721 wrote:

This is homework, and I don't want people to think I'm just hunting for answers. I really don't know how to go about solving these.

Well there you go. I've asked several times for the author/source of the material you're studying, and you've always ignored the question. At least this time you say you don't know the source of the material you're studying...??

@Horace phil,

Ok i may sound stupid here but what is this all about could somebody put it in lamens terms so we're all on the same page???? :~

@salima,

salima;76776 wrote:

why is logic so complicated? isnt it just supposed to be the way the healthy brain works? are there actually different kinds of logic or is it that there are different kinds of logical proofs to show that we are being logical? the only thing i ever saw in the way of a book on logic was something called wff and pruf or something like that, and i didnt get it at all.

To a point it is. Having a healthy brain is a problematic assumption though and the issues arises, however, in what defines a healthy brain? I think that if you narrow the criteria down, it is reasoninglogicallymanyor Bob flying the Kite? Not a well formed formula. The proof on the other hand is the composition used to put a logical statement into form so that we can use inferences and replacement rules to derive the conclusion. This is an example of a logical proof;

@Imnotrussian,

That's sort of my problem too "Imnotrussion." I don't really know what to do Smile

Anyways one of our texts is Hodges' Intro to Elementary Logic and Critical Thinking.

As for the binary connectives, would I be correst in supposing that the 4 are "and" "or" "if/then" and "if and only if"

how do i go about finding whether they are true and consistent?
start making a table? see if there is no occasion wherein the premises are all true and the conclusion false?

@Horace phil,

Horace;76832 wrote:

As for the binary connectives, would I be corre[c]t in supposing that the 4 are "and" "or" "if/then" and "if and only if"

This is a tutorial on the basic connectives, your binary connectives;
http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1454-propositional-logic-symposia-3-disjunction-conditional-biconditional-negation.html
However, I would point out the when use the term "binary connective," you are referring to a more mathematical form of the same thing.

Horace;76832 wrote:

how do i go about finding whether they are true and consistent?
start making a table? see if there is no occasion wherein the premises are all true and the conclusion false?

Again, here is a tutorial on the primary connectives as well as the truth values you are attempting to find;
http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1454-propositional-logic-symposia-3-disjunction-conditional-biconditional-negation.html

Also, here is a tutorial on making a truth tables which addresses most of your concerns;
http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1514-propositional-logic-symposia-6-complex-partial-truth-tables.html

@VideCorSpoon,

I apprecaite the help.
I am familiar with that material but my problem is not that but rather how my questions apply to those principles...

---------- Post added 07-12-2009 at 01:54 PM ----------

Regarding the first question, I think I am looking at [A V -A] -> R but I dont know how to prove R is a logical consequence which is what they are asking...

@Horace phil,

@VideCorSpoon,

VideCorSpoon;76833 wrote:

This is a tutorial on the basic connectives, your binary connectives;
http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1454-propositional-logic-symposia-3-disjunction-conditional-biconditional-negation.html
However, I would point out the when use the term "binary connective," you are referring to a more mathematical form of the same thing.

Again, here is a tutorial on the primary connectives as well as the truth values you are attempting to find;
http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1454-propositional-logic-symposia-3-disjunction-conditional-biconditional-negation.html

Also, here is a tutorial on making a truth tables which addresses most of your concerns;
http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1514-propositional-logic-symposia-6-complex-partial-truth-tables.html

Is he supposed to show that a tautology follows from any set of premises by natural deduction, or by truth-table. Natural deduction is a bit hard, but it is easy to that any argument which has a tautology as a conclusion is a valid argument.
Of course, such an argument must be valid, since it is impossible for it to have true premises and a false conclusion. Vacuously impossible.

@Horace phil,

Well the table would look something like this I think...

A v -A

T T F T
F T T F

And since R is a logical consequence, we have true premises makes a true conclusion, but supposing R were not true, were would have true premises making a false conclusion which wouldn't work.

But I don't see what the point of putting this on a tree would be...

Regarding the other question, I have knocked off the possibilities of "and" or "or" being the connectives, and I know that "if P then P" is a tautology, but I haven't figured how to relate that to the rest of the question...

---------- Post added 07-12-2009 at 03:38 PM ----------

Well, the way I did my truth tables for the second question neitehr "if/then" nor "If and only if" seem to be working...

I had already determined that neither "and" nor "or" would work because p#P had to be a tautology (# being my mysterious connective...)...

P#P has to be a tautology, while Q#P is not a tautological consequence of the sentences P#Q and P...

In a truth table for

([P->Q] ^ P] -> [Q -> P]

I got all T's, as I did when I replaced the "if/then" with "if and only if" which makes them both tautological consequences...

@Horace phil,

Horace;76860 wrote:

Well, the way I did my truth tables for the second question neitehr "if/then" nor "If and only if" seem to be working...

I had already determined that neither "and" nor "or" would work because p#P had to be a tautology (# being my mysterious connective...)...

P#P has to be a tautology, while Q#P is not a tautological consequence of the sentences P#Q and P...

In a truth table for

([P->Q] ^ P] -> [Q -> P]

I got all T's, as I did when I replaced the "if/then" with "if and only if" which makes them both tautological consequences...

Horace, I underestimated the question and may have misled you. For that you have my deep, sincere, heartfelt apology. Sorry.

I incorrectly assumed that the mystery connective ("#") stood in place for one of the commonly used connectives of propositional logic. Propositional logic commonly uses four binary connectives (and, or, if/then, iff) and one unary connective (not).

But there are technically a total of four unary connectives and sixteen binary connectives, as in boolean algebra.

So it appears that your assignment is to find the meaning of the mystery connective ("#") from all the possible binary connectives, not just the four commonly used in propositional logic.

It seems that your mystery connective is that of converse implication, which has the form:

"P ← Q", which is equivalent to P v ~Q

or in the case of

"P ← P", it is equivalent to P v ~P

I will leave it to you to work out the truth table for the other part of the problem, but it does check out.

Horace;76860 wrote:

And since R is a logical consequence

Your first post says that 'A v ~A' is a logical consequence of R, not that R is a logical consequence of 'A v ~A'.

Horace;76860 wrote:

But I don't see what the point of putting this on a tree would be...

The law of the excluded middle is foundational in bivalent classical propositional logic. The point of the question is probably to show that the "P v ~P" form follows from any sentence in propositional logic, and that the sentence tableau method has a specific rule just to allow this in a truth tree, to show that any sentence of the form "P v ~P" follows from any other sentence in propositional logic

@Horace phil,

You deserve marks for your patience VideCorSpoon...How does this look?

A/B | [A v -A] --> R

T/T | T T FT T T
T/F | T T TF F F
F/T | F T TF T T
F/F | F T TF F F

---------- Post added 07-12-2009 at 07:02 PM ----------

I've been doing it backwards...
As goapy pointed out, it's supposed to be [A v -A] as a logical consequence of any sentence R...

So w

---------- Post added 07-12-2009 at 07:03 PM ----------

I've been doing it backwards...
As goapy pointed out, it's supposed to be [A v -A] as a logical consequence of any sentence R...

So we are looking at R -> [A v -A]

---------- Post added 07-12-2009 at 07:06 PM ----------

This is getting a little confusing.
I am going to open a new post to simplify matters...

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