Bee_see
  • Bee_see
The following argument is valid: If Superman were willing and able to prevent evil, he would do so. If Superman were unable to prevent evil, he would be impotent; if he were unwilling to prevent evil, he would be malevolent. Superman does not prevent evil. If Superman exists, he is neither impotent nor malevolent. Therefore, Superman does not exist.
Discrete Math
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Bee_see
  • Bee_see
Bee_see
  • Bee_see
@FibonacciChick666
FibonacciChick666
  • FibonacciChick666
Ok, I'd do a truth table

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FibonacciChick666
  • FibonacciChick666
P is the if part of each statement Q is the then. Write each sentence as a P implies Q. Then negate each. And use the final statement to say well since there is evil, superman can't exist
Bee_see
  • Bee_see
|dw:1444012942048:dw|?
FibonacciChick666
  • FibonacciChick666
more like P-->~Q uh contrapositive I think? Sorry it has been like 4 years since logic. But let me work on this. It will help me with the test I'm studying for
FibonacciChick666
  • FibonacciChick666
SO my first thought, If sup exist then he's not imp. and he's not malev.
Bee_see
  • Bee_see
Hmm, I used the (p imples q) implies (not p or q) table and I got all truth...I want to use the rules of inference though instead of the truth tables. And I'm not sure how.
FibonacciChick666
  • FibonacciChick666
So, since sup can't prevent evil there exists evil--> sup would prevent it but he doesn't-->imp. and malev. BUT that is a contradiction
Bee_see
  • Bee_see
(p implies q) bi conditional statement (not p or q) *
FibonacciChick666
  • FibonacciChick666
and or malev**
Bee_see
  • Bee_see
how would you show that though using the rules of inference. I'm supposed to do a table.I have the premises like this: Superman is willing to prevent evil(W), superman is able to prevent evil (A), superman prevents evil(P), superman is impotent I, superman is malevolent (M), and superman exists(X).
Bee_see
  • Bee_see
|dw:1444013971882:dw|
FibonacciChick666
  • FibonacciChick666
I haven't seen that style before, but my basic argument is, there is evil, it isn't prevented sup isn't I or M --> no sup
FibonacciChick666
  • FibonacciChick666
So let's put it into words, it's essentially a contradiction proof
FibonacciChick666
  • FibonacciChick666
SO I'm looking at these inference rules(Gosh they would have been helpful to see before....Thanks BA-NOT)
FibonacciChick666
  • FibonacciChick666
https://en.wikipedia.org/wiki/List_of_rules_of_inference
FibonacciChick666
  • FibonacciChick666
so this argument is case analysis I think
FibonacciChick666
  • FibonacciChick666
ugh, let me get someone smart here. @dan815 can you fix my mess please?
Bee_see
  • Bee_see
This is how the professors wants it to look if anyone can help:
dan815
  • dan815
sry im here
dan815
  • dan815
are you still working on this The following argument is valid: If Superman were willing and able to prevent evil, he would do so. If Superman were unable to prevent evil, he would be impotent; if he were unwilling to prevent evil, he would be malevolent. Superman does not prevent evil. If Superman exists, he is neither impotent nor malevolent. Therefore, Superman does not exist.
FibonacciChick666
  • FibonacciChick666
yea
dan815
  • dan815
super man is neither impotent nor malevolent
dan815
  • dan815
superman does not prevent evil, so superman is malevolent, so superman cannot exist
Bee_see
  • Bee_see
I have some solutions, but I don't understand then. So for example, after writing all the premises, the person used modus tollens 5 and 4. (5 being not p and 4 being W and A implies p)...I'm not sure how the person knew that modus tollens had to be used.
dan815
  • dan815
hmm lemme see
dan815
  • dan815
just 1 little thing that might come up
dan815
  • dan815
superman does not prevent evil means, either there was no evil to prevent, or he was unable to prevent evil
dan815
  • dan815
but if they say does not prevent evil, that means evil must have took place for him to not prevent it
Bee_see
  • Bee_see
then the person said not W or not A (I'm not sure what rules was used), then M or I (modus ponen....not sure which options). Then not (not M and not I). Came the conclusion that not X. Superman doesn't exist.
dan815
  • dan815
not willing and not able right
Bee_see
  • Bee_see
|dw:1444015956617:dw|
dan815
  • dan815
okay lemme see
dan815
  • dan815
um wait is upside down V or or and
dan815
  • dan815
because not P should be not (W or A) and W and A --> P but they are using the same operators
Bee_see
  • Bee_see
V is or.
Bee_see
  • Bee_see
^ is and.
dan815
  • dan815
okay then isnt there a mistake in there
dan815
  • dan815
yep looks good!
dan815
  • dan815
because not (W or A ) = W and A so it ha to be W and A =>P there
Bee_see
  • Bee_see
can you explain the solution? what rules of inference were used and how?
dan815
  • dan815
what do u mean what step is confusing u
Bee_see
  • Bee_see
the last 6 steps...why use modus tollens for 5 and 4?
dan815
  • dan815
|dw:1444016813628:dw|
dan815
  • dan815
okay there are 2 main ones u need to know
dan815
  • dan815
u can see from truth tables
dan815
  • dan815
|dw:1444016995835:dw|
dan815
  • dan815
this proves not (A and B) = not a or not b
dan815
  • dan815
similiary u can show that not (A or B) = not A and not B
dan815
  • dan815
|dw:1444017343621:dw|
dan815
  • dan815
so these 2 transformations are justified, does that clear it up?
Bee_see
  • Bee_see
what rules were used to do the last 4 steps?
dan815
  • dan815
well we showed how they are equivalent with the truth table
dan815
  • dan815
its just an identity we just showed so its justified
Bee_see
  • Bee_see
My professors wants something like this:
1 Attachment
dan815
  • dan815
|dw:1444017601337:dw|