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princesspixie
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please tell me if this is correct:
“All mathematicians must be good logicians and all good logicians must justify their claims.”
 2 years ago
 2 years ago
princesspixie Group Title
please tell me if this is correct: “All mathematicians must be good logicians and all good logicians must justify their claims.”
 2 years ago
 2 years ago

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princesspixie Group TitleBest ResponseYou've already chosen the best response.0
a) 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
 2 years ago

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
p: 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
 2 years ago

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

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

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

satellite73 Group TitleBest 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
 2 years ago

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

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

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

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

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

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

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

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

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

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
¬(p⟹q)∧(q⟹r) ?
 2 years ago

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

satellite73 Group TitleBest 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
 2 years ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
means "not"
 2 years ago

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

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

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
is 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.
 2 years ago

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

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
if 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"
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
ok I understand
 2 years ago

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
then 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
 2 years ago

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i forget what C is
 2 years ago

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the 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
 2 years ago

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

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

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
ok I see
 2 years ago

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the 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
 2 years ago

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

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

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
thanks so much for all your help!!
 2 years ago
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