1)

(a)Our Mishnah needs to add the case of 'Shenayim ... ve'Ein Notlin Reshus' - to teach us that even if they were Mevatel Reshus to one of the two men who forgot to participate in the Eruv, on the express condition that he is Mevatel to his friend, the second Bitul is ineffective. Why is that? Because at the time when he acquired the rights, they were not really his to give away, and the fact that he is the agent of those who were Mevatel Reshus to him is meaningless.

2)

(a)The Beraisa, which states 'Echad she'Lo Erav Nosen Reshuso le'Echad she'Erav' - must be speaking when there was a third person (otherwise, with whom is he making an Eruv?) Nevertheless, the Beraisa clearly permits being Mevatel to just one of the two - a Kashya on Rabah.

(b)The Seifa, which states 'Aval Ein Echad she'Erav Nosen Reshuso le'Echad she'Lo Erav', speaks, according to Rabah, when the second person who did not make an Eruv is still alive ('Ha Ke'de'Isa, ve'Ha Ke'de'Isa').

(c)The Seifa de'Reisha reads 'u'Shenayim she'Irvu Nosnin Reshusan li'Shenayim she'Irvu', from which we can deduce 'but not to one of them' - a proof for Rabah.

(d)If the Beraisa means to say 'le'Echad mi'Shenayim', counters the Gemara - then the Tana should have said 'le'Echad she'Eirav O le'Echad she'Lo Eirav' (and we know that, since an Eruv was made, there must be at least two people).

3)

(a)Abaye establishes the Beraisa 'Echad she'Erav Nosen Reshuso le'Echad she'Erav' - when the third person is still alive, the Chidush being that it is not necessary to be Mevatel Reshus to each resident independently.

(b)According to Rabah, the Beraisa speaks when the third person died - the Chidush is that we do not decree (to forbid being Mevatel to one person whenever there where once two) because of a case when that person is still alive (because people will think that there too, it is in order to be Mevatel to just one of them).

(c)The Chidush of 'Shenayim she'Irvu Nosnin Reshusan le'Echad she'Lo Erav' - is that we do not penalize the one who forgot to participate in the Eruv.

(d)According to Abaye, 'Shenayim she'Lo Irvu, Nosnin Reshusan li'Shenayim (meaning 'le'Echad mi'Shenayim') she'Irvu' comes to teach us - that Chazal did not decree, on the grounds that if we permit two to be Mevatel Reshus to one, maybe people will also do the reverse, and permit one person to be Mevatel Reshus to two.

4)

(a)

1. ... 'Shenayim she'Lo Irvu, Nosnin Reshusan ... O le'Echad she'Lo Eirav' comes to teach us - that even though none of them made an Eruv, Bitul Reshus is still effective, and that Chazal did not penalize them (to ensure that the institution of Eruv does not become forgotten).

2. ... 've'Ein Shenayim she'Irvu Mevatlin Reshusan li'Shenayim she'Lo Irvu' comes to teach us that - even if the first of the latter two was Mevatel Reshus to the second, it does not help, since it was not his Reshus to be Mevatel (catch 22 situation).

3. ... 've'Ein Shenayim she'Lo Irvu, Nosnin Reshusan li'Shenayim she'Lo Irvu' comes to teach us that - the previous case is not even effective if those who were Mevatel Reshus did so on the express condition that he is Mevatel to his friend (as we explained in 1).

5)

(a)A heir whose father died on Shabbos may possibly not be able to be Mevatel Reshus - since, due to the fact that he did not own the property yesterday, he could not have made an Eruv then, and, someone who was not able to make an Eruv yesterday, cannot be Mevatel Reshus.

(b)Rav Nachman holds that he may - because a son is always called the 'leg of the father' (i.e. he stands in his father's place and takes over all his fathers rights).

6)

(a)According to Rav Nachman, when the Beraisa states 'Chutz mi'Mevatel Reshus' - it means 'Chutz mi'Toras Bitul Reshus', incorporating both the Mevatel Reshus and his son.

(b)'Kol she'Mutar le'Miktzas Shabbos, Hutar le'Chol ha'Shabbos' - refers to a case of someone who made an Eruv via a door or a window which caved in or became blocked on Shabbos.

(c)We will not know the case of the Lechi or the Korah fell from the previous case - because there the Mechitzos at least, are still standing, whereas here, even the Mechitzos (the Lechi or the Koreh) are no longer standing. So we need 'Zeh ha'Klal', to include it. (It would appear that, according to those who hold that Lechi or Korah Mishum Heker, it is even more difficult to learn from the previous case, since here, in the middle of Shabbos it will transpire that there is suddenly no Heker to remind him not to carry out into the street. Consequently, it will certainly requires 'Zeh ha'Klal' to teach us that Hutar le'Chol ha'Shabbos'.)

7)

(a)'Kol she'Ne'esar le'Miktzas Shabbos, Ne'esar le'Chol ha'Shabbos' - refers to the case of two houses on opposite sides of the street, when gentiles fenced off the street on both sides, forming a sort of Chatzer.

(b)We would not have known the case when the gentile who shared the Chatzer with other Jewish residents died, from the previous one - because whereas in the previous case, there was no way of permitting carrying from the two houses into the street, in the case when the gentile died, it was possible to rent the gentile's rights in the Chatzer before Shabbos.

8)

(a)If someone from the Chatzer died, having bequeathed his Reshus to someone who lived outside the Chatzer ...

1. ... before Shabbos - that beneficiary is not included in the Eruv, and forbids all the residents of the Chatzer to carry from their houses into the courtyard.

2. ... after Shabbos has already come in - they are permitted to carry, because of the principle 'Kol she'Mutar le'Miktzas Shabbos ... '

(b)if someone from outside the Chazter, who had owned a section of the Chatzer, died, having bequeathed that section to a resident of the Chatzer ...

1. ... before Shabbos - the residents of the Chatzer will be permitted to carry, since the beneficiary will participate in the Eruv before Shabbos comes in.

2. ... after Shabbos had already come in - the beneficiary will forbid all the other residents to carry.

(c)According to Rav Nachman (who holds that Yoresh Mevatel) - when the Beraisa says 'Oser' it means without Bitul Reshus, but it goes without saying that Bitul Reshus will be effective.