anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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.
anonymous
  • anonymous
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"?
anonymous
  • anonymous
@princesspixie Does this help?

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anonymous
  • anonymous
a little but what does a dis junction mean?
anonymous
  • anonymous
Disjuntion isn't mentioned, but I'd assume it's two propositions combined with 'or'.
anonymous
  • anonymous
oh i meant to say conjunction sorry!
anonymous
  • anonymous
conjunction is when you take two propositions and combine them with and or or.
anonymous
  • anonymous
but the sentence already has the word and in it so thats why im confused..
anonymous
  • anonymous
Which just means you use and \( \wedge\) for it.
anonymous
  • anonymous
??
anonymous
  • anonymous
can you give me an example..
anonymous
  • anonymous
this would be the first answer ? : “All mathematicians must be good logicians ^ good logicians must justify their claims.”
anonymous
  • anonymous
No, because you need to convert them into conditionals.
anonymous
  • anonymous
“if you are a mathematicians then you must be a good logician and all good logicians must justify their claims.” ??
anonymous
  • anonymous
Yeah, now I'd say that \(p\) means 'person is mathematician' \(q\) means 'person is good logician' and \(r\) means 'justifies their claims'
anonymous
  • anonymous
So we end up with \[ (p \implies q)\wedge(q \implies r) \]
anonymous
  • anonymous
ok, is that part of the answer?
anonymous
  • anonymous
That is part a.
anonymous
  • anonymous
ok, great thanks! how would i negate it now? just throw a not in front of the original sentence?
anonymous
  • anonymous
Yeah, throw in a \( \lnot \) .
ganeshie8
  • ganeshie8
and you may have to simplify
ganeshie8
  • ganeshie8
\( \neg ( ( p \implies q ) \wedge ( q \implies r ) ) \) \( \neg ( p \implies q ) \vee \neg ( q \implies r ) \) \( (p \wedge \neg q) \vee (q \wedge \neg r) \)
ganeshie8
  • ganeshie8
which means, the statement is true, whenever a 'mathematician is not a logician' or whenever a 'logician is not a justfier'
ganeshie8
  • ganeshie8
which forms a logical negation of the original statement
anonymous
  • anonymous
ok thank you :)
ganeshie8
  • ganeshie8
np.. yw :)
anonymous
  • anonymous
so should the negation be : a mathematician is not a good logicians and logicians do not justify claims ?
anonymous
  • anonymous
needs to be an or in the middle
anonymous
  • anonymous
so would it be : a mathematician is not a good logician or logicians would justify their claims?
anonymous
  • anonymous
@wio

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