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Ok, I'd do a truth table
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
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
SO my first thought, If sup exist then he's not imp. and he's not malev.
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.
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
(p implies q) bi conditional statement (not p or q) *
and or malev**
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).
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
So let's put it into words, it's essentially a contradiction proof
SO I'm looking at these inference rules(Gosh they would have been helpful to see before....Thanks BA-NOT)
so this argument is case analysis I think
sry im here
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.
super man is neither impotent nor malevolent
superman does not prevent evil, so superman is malevolent, so superman cannot exist
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.
hmm lemme see
just 1 little thing that might come up
superman does not prevent evil means, either there was no evil to prevent, or he was unable to prevent evil
but if they say does not prevent evil, that means evil must have took place for him to not prevent it
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.
not willing and not able right
okay lemme see
um wait is upside down V or or and
because not P should be not (W or A) and W and A --> P but they are using the same operators
V is or.
^ is and.
okay then isnt there a mistake in there
yep looks good!
because not (W or A ) = W and A so it ha to be W and A =>P there
can you explain the solution? what rules of inference were used and how?
what do u mean what step is confusing u
the last 6 steps...why use modus tollens for 5 and 4?
okay there are 2 main ones u need to know
u can see from truth tables
this proves not (A and B) = not a or not b
similiary u can show that not (A or B) = not A and not B
so these 2 transformations are justified, does that clear it up?
what rules were used to do the last 4 steps?
well we showed how they are equivalent with the truth table
its just an identity we just showed so its justified