A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
please tell me if this is correct:
“All mathematicians must be good logicians and all good logicians must justify their claims.”
 2 years ago
please tell me if this is correct: “All mathematicians must be good logicians and all good logicians must justify their claims.”

This Question is Closed

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0a) Write this statement symbolically as a conjunction of two conditional statements. Use three components (p, q, and r) and explicitly state what these are in your work. Remember: a component in logic is a simple declarative sentence that is either true or false. For example, "You are a student in MAT 101" would be a component statement. Note how this sentence contains no logical connectives like "not", "or", "and", etc. b) Write the negation of this statement symbolically. Explain your reasoning here. c) Now use part b) to write the negation of this statement verbally. A p means 'person is mathematician' q means 'person is good logician' and r means 'justifies their claims' (p⟹q)∧(q⟹r) B (~p⟹~q)∧(~q⟹~r) You put the ~ mark because that negates the statement. C  If a person is not a mathematician then the person is not a good logician or they do not justify their claims

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0The Boxes are arrows

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1p: a person is a good mathematician q: a person is a good logician \(p\implies q\) : if a person is a good mathematician, then a person is a good logician rather tortured english, would probably say if a person is a good mathematician then he or she is also a good logician

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0what would the r statement be?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\(q\implies r\) : if a person is a good logician, then they justify their claims

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0would i say r: person justifies their claims

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[(p\implies q)\land (q\implies r)\] take those two statements and stick the word "and" between them

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0what do you mean those two statements and stick an and?

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0^ is the symbol for and?

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0ok is the negation correct?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1if a person is a good logician, then they justify their claims and if a person is a good logician, then they justify their claims

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0thats the negation ?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1no that is \[(p\implies q)\land (q\implies r)\]

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0ok would I see.. would I put a ~ before the q and the r to negate it ?

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0or infront of all the letters?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1no you have to put \(\lnot\) in front of the whole thing

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0what is the explanation for that ?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[\lnot\left((p\implies q)\land (q\implies r)\right)\] then you should rewrite without the \(\implies \) and use demorgan laws

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0I dont understand..

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1it will take a while do you know that \(p\implies q\equiv \lnot p\lor q\)?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1to negate a statement you put a big \(\lnot\) in front of the whole thing, you do not negate each piece separately

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0ok how do I explain the reasoning for it?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1you have some statement "blah blah blah" the the negation is "it is not true that blah blah blah"

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1if you want to negate it you have to rewrite it as \[(\lnot p \lor q)\land (\lnot q\lor r)\] then negate it as \[\lnot \left((\lnot p \lor q)\land (\lnot q\lor r)\right)\]

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0so both should be included in the answer?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1yes but we have more work to do

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0Im still not sure how I should explain the answer ..

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1unless you are unfamiliar with these laws. perhaps you are supposed to do something else

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1your original statement All mathematicians must be good logicians and all good logicians must justify their claims is correct

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0ive never seen that little hook thing, but i see that in the textbook it says converse inverse and contrapostive .. not sure if that helps

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1actually i would get rid of the word "must"

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1"all mathematicians are good logicians and all good logicians justify their claims" perhaps is better

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0thats why i thought this symbol would be in the equation ~

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\(\lnot\) is the same as ~

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0ok so should i use the ~ if that what the text book uses?

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0ok .. how should i explain that in simple terms?

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0is this good... The symbol ~ means not. Therefore, if a person is not a good mathematician then the person is not a good logician, and the person cannot justify their claims.

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1i would think perhaps the negation, without using the symbols, would be not all mathematicians are good logicians or not all logicians justify their claims

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0ok so i should use that instead of if a person is not a good... ?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1if a person is a good mathematician, then they are a good logician the statement if a person is not a good mathematician then the person is not a good logician is not the negation, it is the "inverse"

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0so would that be a good explanation?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1then negation of "if a person is a good mathematician, then they are a good logician" is there is some mathematician who is not a good logician

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0thats the answer for C?

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0c) Now use part b) to write the negation of this statement verbally.

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1the negation of the whole thing would read something like "there is a good mathematician who is not a good logician, or there is a good logician who does not justify their claims

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1the negation of the "and" statement is one or the other is false

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1really to do this symbolically takes a while

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[\lnot \left((\lnot p \lor q)\land (\lnot q\lor r)\right)\] \[\lnot(\lnot p\lor q)\lor \lnot(\lnot q \lor r)\] \[(p\land \lnot q)\lor (q\land \lnot r)\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1the last statement says there is a good mathematician who is not a good logician or there is a good logician who does not justify their claims

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0oh i see ok thanks!!

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1yw good luck with this

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0thanks so much for all your help!!
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.