Logic and set theory

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TJR

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If p, q, and r are propositions, determine the following compound statements are tautology, contradiction, or neither.

(a) [(p ) q) ^ (q ) r)] ) (p ) r)

(b) (p ^ :q) ^ (p ^ q)
 
TJR said:
If p, q, and r are propositions, determine the following compound statements are tautology, contradiction, or neither.

(a) [(p ) q) ^ (q ) r)] ) (p ) r)

(b) (p ^ :q) ^ (p ^ q)
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Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
Must say that your notation is strange to me.

Do you mean

[MATH][(p \lor q) \land (q \lor r) \implies (p \lor r)[/MATH]
and

[MATH](p \land \neg q) \land (p \land q)[/MATH]
 
I assume these are:

[MATH][(p \rightarrow q) \land (q \rightarrow r)] \rightarrow (p \rightarrow r)[/MATH]
[MATH](p \land \lnot q) \land (p \land q)[/MATH]
Just draw up a truth table for each and examine what Truth values the statements take, to determine whether they are tautologies, contradictions or neither.
In fact they're easy to work out just by thinking about them.
 
TJR said:
If p, q, and r are propositions, determine the following compound statements are tautology, contradiction, or neither.
(a) [(p ) q) ^ (q ) r)] ) (p ) r)
(b) (p ^ :q) ^ (p ^ q)
Click to expand...
Be honest, do any of you who have answered have any real idea what the notation in this post means?
 
pka said:
Be honest, do any of you who have answered have any real idea what the notation in this post means?
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No. That is why I asked what it meant. I tend to ask for clarification when I do not understand a question. I view that as a courteous thing to do in that circumstance. What would you advise?
 
JeffM said:
What would you advise?
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Jeff I do agree that we should not ever have to guess as to what a post means.
My advise is: ask the student to name the textbook and author(maybe most important) so that we know the notation is used.
Then I would ask the student to post the question exactly as it appears in the textbook , not changing symbols but using English words such as union, intersection, negation, etc.
In this case, I think that unless the original post can be so clarified, this thread should closed.
 
TJR said:
If p, q, and r are propositions, determine the following compound statements are tautology, contradiction, or neither.

(a) [(p ) q) ^ (q ) r)] ) (p ) r)

(b) (p ^ :q) ^ (p ^ q)
Click to expand...
I strongly suspect that lex's guess is right:
lex said:
I assume these are:

[MATH][(p \rightarrow q) \land (q \rightarrow r)] \rightarrow (p \rightarrow r)[/MATH]
[MATH](p \land \lnot q) \land (p \land q)[/MATH]
Click to expand...
You probably used ")" as a substitute for "\(\supset\)" meaning implication. Clearly, that was not a good choice.

I've been hoping you would respond by indicating which guess, if any was correct, and providing an image either of the problems as printed, or your handwritten version (or, as pka suggested, writing it out in words). Once the meaning is cleared up, we can start actually helping (assuming the help already given wasn't enough).
 
Dr.Peterson said:
You probably used ")" as a substitute for "\(\supset\)" meaning implication. Clearly, that was not a good choice.
Click to expand...
If that is the case, then then the source is using Copi's notion \(p\supset q\) means \(p\text{ implies }q\)
 
pka said:
Jeff I do agree that we should not ever have to guess as to what a post means.
My advise is: ask the student to name the textbook and author(maybe most important) so that we know the notation is used.
Then I would ask the student to post the question exactly as it appears in the textbook , not changing symbols but using English words such as union, intersection, negation, etc.
In this case, I think that unless the original post can be so clarified, this thread should closed.
Click to expand...
@pka

Sometimes I think I get my back up unnecessarily at the way you say things. Probably foolish of me.

In a perfect world, we should never have to guess what a problem means. However, we have a huge variety of people asking us questions, some quite young, some quite unsophisticated. Moreover, unless you know LaTex or know how to import images into this site, it can be difficult to express mathematical notation. Furthermore, a lot of badly posed questions derive from inept paraphrases, which often represents an actual failure to understand the real problem posed. Seeing an incoherent paraphrase actually facilitates identifying that the fundamental issue is a failure to understand what the problem even is.

In short, I do not think that a site like this can reasonably have high expectations for the quality of the first few questions asked by someone. We are going to get a lot of badly posed questions and must tolerate them.

With that said, I would agree that our tolerance for inept questions should depend in part on the mathematical level of the question. If someone is asking a question about differential equations, the question should be better posed than one on finding a least common denominator. And propositional calculus ought not, and used not to, be something taught to freshman in high school, but the style now seems to be to dump introductory smatterings of disparate topics into high school math. So I have no idea whether this poster is some 14 year old subjected to the latest fad of the education majors or a college philosophy major who should know better.

I like your idea about asking the original poster to translate any mathematical symbols that they cannot type into English equivalents. One advantage of this is that students are sometimes vague about what certain symbols mean. Identifying that as a problem has value in itself. Another advantage is that it would expedite finding out what the problem actually is.

Your idea of asking for the name and edition of the text along with the page number seems to me less useful. Unless you happen to have that edition of that text, receiving the information requested merely delays getting clarification.
 
Do you know how to draw up a truth table to test these statements?
 
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