Due to Guilherme who steered and translated the issue into English! This downside was requested on the seventeenth Brazilian Mathematical Olympiad of Public Faculties. It went viral on social media as a result of folks mentioned what the right reply must be.
Assume that each of the next sentences are true:
• Pinocchio at all times lies;
• Pinocchio says, “All my hats are inexperienced.”
We are able to conclude from these two sentences that:
(A) Pinocchio has a minimum of one hat.
(B) Pinocchio has just one inexperienced hat.
(C) Pinocchio has no hats.
(D) Pinocchio has a minimum of one inexperienced hat.
(E) Pinocchio has no inexperienced hats.
As ordinary, watch the video for an answer.
Brazilian Olympiad Pinocchio’s Inexperienced Hats Viral Query
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Reply To Brazilian Olympiad Pinocchio’s Inexperienced Hats Viral Query
(Just about all posts are transcribed shortly after I make the movies for them–please let me know if there are any typos/errors and I’ll right them, thanks).
We all know Pinocchio at all times lies, so he solely speaks mathematically false statements. The assertion “All my hats are inexperienced” is fake if some hat isn’t inexperienced. The assertion is unquestionably deceptive–and maybe a real-world “lie”–if Pinocchio has no hats. These choices correspond to reply decisions (A) and (C). We’ll analyze reply selection (C) in additional element beneath.
(A) Pinocchio has a minimum of one hat.
(C) Pinocchio has no hats.
However first let’s study the opposite decisions one after the other.
(B) Pinocchio has just one inexperienced hat.
Is that this at all times true? No. Think about Pinocchio has 2 inexperienced hats and 1 blue hat. He may communicate a false assertion that he has all inexperienced hats. Thus selection (B) is incorrect.
(D) Pinocchio has a minimum of one inexperienced hat.
Think about Pinocchio has 2 blue hats. He may deceive say he has all inexperienced hats. Thus reply (D) isn’t right.
(E) Pinocchio has no inexperienced hats.
If Pinocchio has 1 inexperienced hat and 1 blue hat he can be mendacity to say he has all inexperienced hats. Thus (E) can be incorrect.
Most individuals conform to remove (B), (D), and (E). However aren’t each (A) and (C) right solutions?
No! From a logical perspective, reply selection (C) is incorrect.
Vacuously true statements
An announcement is vacuously true if the premise is fake or can’t be achieved. For instance, contemplate a room with no cell phones. If somebody says, “All cell phones within the room are turned OFF,” then that may technically be a real assertion. In spite of everything, there aren’t any cell phones within the room, so one may say all the ones within the room are turned off. However for a similar motive, one may additionally communicate a vacuously true assertion, “All cell phones within the room are turned ON.”
Each statements are technically true, however they’re meaningless as a result of there are literally no cell phones within the room.
Let’s apply the precept to the Pinocchio downside.
(C) Pinocchio has no hats.
If Pinocchio has no hats, then any assertion he makes concerning the hats is vacuously true. Thus the assertion, “All my hats are inexperienced” is technically a real assertion. However we all know Pinocchio at all times lies, so that is an impossibility.
Subsequently, Pinocchio can’t don’t have any hats; he will need to have a minimum of one hat. We are able to remove reply selection (C) and the one right reply is (A) Pinocchio has a minimum of one hat.
References
Pinocchio downside articles
https://sivtelegram.media/students-make-memes-involving-pinocchio-and-leak-reactions/
https://brainly.com.br/tarefa/52854041
Pinocchio illustration
https://en.wikipedia.org/wiki/File:Pinocchio.jpg
Bram28 clarification vacuously true
https://math.stackexchange.com/questions/2723860/still-struggling-to-understand-vacuous-truths
Wikipedia vacuous fact
https://en.wikipedia.org/wiki/Vacuous_truth
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