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1. Whenever a Mishnah (or Gemara) says that one is "Patur" if he does something on Shabbos, it means that the act is forbidden, but he is exempt from punishment.
2. Shmuel states three exceptions to this rule (#1).
3. If two people do a Melachah together, they are not obligated to bring a Korban Chatas.
4. If one gave another person an object, and the second person then went from a private domain to a public domain, he is liable.
5. Abaye extrapolates from the Mishnah that a person's hand is considered neither a private domain nor a public domain.
A BIT MORE
1. Shmuel explains that "Patur" ("exempt") said with regard to a law Shabbos does not mean that the Tana (or Amora) is saying that the act is permitted. Rather, it means that one is exempt from bringing a Korban if he did the act accidentally, but that the act is prohibited (at least according to Rabbinic law).
2. They are: One who closes his door and finds that he has trapped a deer in his house, one who traps a dangerous snake, and one who makes a hole in a painful, pus-filled blister.
3. This is derived from the verse, "when he will do it," implying that one is liable only when he transgresses the entire prohibition himself, but not when he does the act together with someone else.
4. This is despite the fact that the Mishnah states that if a poor person withdraws his hand back into the public domain after the homeowner puts an object into it, he is not liable. The difference is that the poor person merely has his hand in the private domain, and a hand is not considered "at rest," as opposed to when one's entire body is in one domain (and then he exits with the object).
5. For example, it is apparent from the fact that the poor person is exempt after he takes the object from the homeowner's hand (as in #4 above) that the homeowner's hand is not considered a private domain. Otherwise, the poor person would be liable when he brings his hand back into the public domain. (The same proof applies regarding the opposite case in the Mishnah to show that a hand is not considered a public domain.)
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