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princesspixie
Group Title
Consider the following statement:
“All mathematicians must be good logicians and all good logicians must justify their claims.”
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.
b) Write the negation of this statement
 2 years ago
 2 years ago
princesspixie Group Title
Consider the following statement: “All mathematicians must be good logicians and all good logicians must justify their claims.” 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. b) Write the negation of this statement
 2 years ago
 2 years ago

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wio Group TitleBest ResponseYou've already chosen the best response.1
Okay, so suppose we have the form: "All p must be q". The question is does this mean \(p\implies q\) or \(q \implies p\)? You have to test it out a bit.
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
So I'd start out with something like... "All dogs must be animals". Now does this mean "If you're a dog, then you're an animal." or does it mean "If you're an animal, you must be a dog"?
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
@princesspixie Does this help?
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
a little but what does a dis junction mean?
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
Disjuntion isn't mentioned, but I'd assume it's two propositions combined with 'or'.
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
oh i meant to say conjunction sorry!
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
conjunction is when you take two propositions and combine them with and or or.
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
but the sentence already has the word and in it so thats why im confused..
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
Which just means you use and \( \wedge\) for it.
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
can you give me an example..
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
this would be the first answer ? : “All mathematicians must be good logicians ^ good logicians must justify their claims.”
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
No, because you need to convert them into conditionals.
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
“if you are a mathematicians then you must be a good logician and all good logicians must justify their claims.” ??
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
Yeah, now I'd say that \(p\) means 'person is mathematician' \(q\) means 'person is good logician' and \(r\) means 'justifies their claims'
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
So we end up with \[ (p \implies q)\wedge(q \implies r) \]
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
ok, is that part of the answer?
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
That is part a.
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
ok, great thanks! how would i negate it now? just throw a not in front of the original sentence?
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
Yeah, throw in a \( \lnot \) .
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
and you may have to simplify
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
\( \neg ( ( p \implies q ) \wedge ( q \implies r ) ) \) \( \neg ( p \implies q ) \vee \neg ( q \implies r ) \) \( (p \wedge \neg q) \vee (q \wedge \neg r) \)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
which means, the statement is true, whenever a 'mathematician is not a logician' or whenever a 'logician is not a justfier'
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
which forms a logical negation of the original statement
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
ok thank you :)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
np.. yw :)
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
so should the negation be : a mathematician is not a good logicians and logicians do not justify claims ?
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.1
needs to be an or in the middle
 2 years ago

princesspixie Group TitleBest ResponseYou've already chosen the best response.0
so would it be : a mathematician is not a good logician or logicians would justify their claims?
 2 years ago
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