I know this question has already been posted but I cannot seem to find an answer there.I am taking this course and I just cannot figure out how to solve this on the platform. Please I really need help with this. The link to the platform is: .  Thanks in advance I would trully be grateful to the person who tells me how to solve this on the given website. Thanks in advance!
I'm having trouble solving a Fitch Style Proof and I was hoping someone would be able to help me.  Premises: p ∧ q  Goal: q ∨ r  Would be an assumption (p ∧ q => q ∨ r) in first step a correct one?   Then, q ∨ r Implication Elimination: 2, 1  Why is it not correct?  Thank you very much for any help!
I'm bugged by the following that's summarized on p. 109 of .     False theorem: All horses are the same color.      Proof by induction:      $\fbox{$P(n)$ is the statement: In every set of horses of size $n$, all $n$ horses are the same color.}$   $\fbox{Base Case or $P(1)$:}$ One horse is the same color as itself. This is true by inspection.   $\fbox{Induction Step:}$ Assume $P(k)$ for some $k \geq 1$.   $\fbox{Proof of $P(k + 1) :$}$   Since $\{H_1, H_2, ... , H_n\}$ is a set of $n$ horses, the induction hypothesis applies to this set. Thus, all the horses in this set are the same color.   Since $\{H_2, H_3, ... , H_{n+1}\}$ is also a set of $n$ horses, the induction step likewise holds for this set. Thus, all the horses in this set are the same color too.         Therefore, all $n +1$ horses in $\{H_1, H_2, H_3, ... , H_n , H_{n+1}\}$ are the same color. QED.   The issue the instructor was trying to point out is clearly valid. For the case $n = 1$, there is only ${H_1}$. So this case says nothing about possible overlapping elements of each set of $(n + 1)$, for instance $H_2$ in the above proof.    But it was proposed in the class discussion that this was the only problem. Had you been able to prove $P(2)$ true, then a proof of the above format would have been fine.    My interpretation is that yes, you could prove all horses are the same color, if you can prove that any set of two horses will be the same color. But this format would not work.  Why not? The problem I see is that the above proof is for the existence of at least one particular pair of sets of horses of sizes $n$ and $n + 1$, such that in each set, all horses are the same color.  Particularly when the set of size $n$ is a subset of the set of size $n + 1$.  In order to prove the induction step, don't you need to prove that sets of sizes $n$ and $n + 1$, do not necessarily contain the same, overlapping elements?  You could prove that any horse can be added to a set of 2 horses.  Take the last two, and they must be the same color, and so on.  Wwhatever color the first two happen to be, all other horses must thus be the same color.    Am I misinterpreting the example, or am I making a logical error? Thanks in advance. I was playing modern with the owner of a shop.  He played a  which he used to bring in 7 lands: 5 basic mountains and 2  cards.  He then claimed that each  triggered 5 times (killing me).  I am doubting this now.    Here is my reason: The two  cards entered at the same time as the other 5 basic lands.  That means when they were on the battlefield and their ability was in effect, the other 5 basic lands were already there too.  That seems too late to trigger a "Enters the Battlefield" effect.  So here is my question.  Am I right or wrong?  If I am wrong, please show me how the enter the battlefield effect can trigger for something that enters the battlefield at the same time as itself.  If I am right, please show me the rules that prove it.  I now have two shop owners that are convinced that this is a legal play.  If it is not legal, I am going to need clear rules citations to convince them.    Side note:  If I am wrong and it is a legal play, then I have a follow up scenario.  Say I have 2  cards and 5 other human cards in my graveyard.  If I play a spell that lets me return all of them to the battlefield at the same time (say ), would the  cards get 6 +1/+1 counters on them?    To me, if the trick that was played on me with  is legal then my  cards should also get the +1/+1 counters. I would like to know how to put a time delay in a Python script. 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