1)

(a)Rabah and Rav Yosef establish the Machlokes between the Tana Kama in our Mishnah (who validates the Eruv in the tower whose key is lost) and Rebbi Eliezer (who does not), by a wooden tower - According to them, the Tana Kama considers a wooden cupboard to be a vessel, to which we apply the principle 'Ein Binyan u'Setirah be'Kelim' (in which case, one is permitted to break it, in order to get to the fruit); whereas Rebbi Eliezer considers it to be an Ohel, to which Binyan and Setirah apply. Since the Tana Kama permits breaking the cupboard, the Eruv is accessible, and is therefore in the same Reshus as the owner.

(b)Rabah and Rav Yosef contend that a Zav can transmit Tum'as Heset to a vessel, but not to an Ohel. Consequently, the Tana Kama of the Mishnah in Zavin, who renders a large cupboard on which a Zav banged, Tamei, must hold like the Tana Kama of our Mishnah, who considers a cupboard to be a vessel; whereas Rebbi Nechemyah and Rebbi Shimon, who declare it Tahor, consider it an Ohel, like Rebbi Eliezer.

(c)The Zav must have banged the cupboard - with his gloved fist or with a flat wooden vessel, which do not transmit Tum'ah through mere contact. Because had he banged it with his bare fist, it would be Tamei through contact with a Zav, and not through Heset (moving).

2)

(a)Based on the Beraisa in Zavin, Abaye learnt that a Zav can even be Metame (be'Heset) an Ohel.

(b)If the object moves directly due of the Zav's force, then anything, even an Ohel, becomes Tamei; but if it moves only as a result of the vibrations, it does not.

(c)According to Abaye, the Machlokes Tana'im in the Mishnah in Zavin is when the cupboard which the Zav banged did not actually move, but only vibrated: the Tana Kama compares this to moving it directly, and it is Tamei; whereas Rebbi Nechemyah and Rebbi Shimon compare it to causing vibrations, which in turn, cause things to move, in which case it remains Tahor.

3)

(a)Abaye and Rava (who establish our Mishnah by a wooden tower) explain - that the lock whose key has been lost is tied with a rope which now needs to be cut. The Tana Kama, who validates the Eruv, considers it accessible, because he holds like Rebbi Yossi, who allows one to take vessels on Shabbos (with a couple of notable exceptions), to use for anything that is permissible; whereas Rebbi Eliezer holds like Rebbi Nechemyah, who forbids taking a vessel for any purpose other than for the one for which it was made. Consequently, since no knife is specifically made for cutting the rope that ties locks, it is not possible to gain access to the Eruv on Shabbos.

(b)There no Isur d'Oraysa per se in cutting the rope - since it is merely Kilkul (because it spoils the rope).

(c)It will not however, be permitted to cut the rope on Shabbos, because, due to the resemblance to the Melachah of Soser, Chazal forbade it. However, it is not forbidden during Bein Hashemashos of Erev Shabbos - since the Tana holds like Rebbi. Consequently, the Eruv is valid.

4)

(a)The Eruv becomes invalidate, if it rolls away before Shabbos - only if it rolled at least four Amos outside the Techum Shabbos.

(b)If a pile of stones fell on the Eruv, or it got burnt, or if it was Terumah and became Tamei - it becomes invalid.

(c)The pile of stones renders the Eruv invalid - not because it is Muktzeh, but because they are heavy stones which require tools to remove them, thus making this a Melachah d'Oraysa (I am not certain why), and even Rebbi will agree that doing so is forbidden during Bein Hashemashos, and the Eruv is invalidated.

(d)Should any of these occur on Shabbos, the Eruv is valid, since it was still intact when Shabbos entered.

5)

(a)'Harei Zeh Chamar Gamal' - means that, not only is the Eruv invalid, but that one cannot even walk from his house in the opposite direction from the Eruv - only in between his residence and the Eruv (taking into account both Chumros: of what would have been forbidden had the Eruv been effective, and had it not). The connotation of the name is like someone who tries to leads a donkey and a camel at the same time: one normally walks behind the donkey, but in front of a camel, so how does one handle them both simultaneously?

(b)Rebbi Yossi and Rebbi Shimon - quote five elders who say that a Safek Eruv is valid.

(c)Had the Tana just mentioned an Eruv that rolled away - we would have said that that case becomes invalid because it is no longer there with him, whereas the Eruv which is buried under a pile of rubble is (so perhaps it remains valid). On the other hand, had it mentioned only the latter case, we would have said that the Eruv is invalid there, because it is covered, which is not the case by the Eruv that rolled away.

(d)The Tana mentioned the case when the Eruv got burnt - to show the extent of Rebbi Yossi, who validates the Eruv even though it is no longer in existence; and it mentions the case when it became Tamei - to show the extent of Rebbi Meir, who invalidates it even though it is.

6)

(a)Rebbi Meir agrees that a Tamei person who is in doubt whether he Toveled or not, remains Tamei - by a Tum'ah d'Oraysa.

(b)By a Tum'ah de'Rabbanan e.g. if he ate half a Peras of Tamei food, or if he entered with his head and most of his body into a bath of drawn water, and then, in either case, he Toveled in such a way that his Tevilah was a Safek - Rebbi Meir holds that he is Tahor mi'Safek .

(c)According to Rebbi Yossi, he is Tamei even if his Tum'ah was only a Tum'ah de'Rabbanan.

(d)The Mishnah incorporates in this Din someone who knows for certain that he Toveled, but he is not sure whether the Mikveh in which he Toveled contained forty Sa'ah or not; or if there were two Mikva'os, one of which contained forty Sa'ah, whilst the other did not, and he does not know in which Mikveh he Toveled.

7)

(a)Rebbi Meir is stringent with regard to Tevilah in the cases of d'Oraysa. Why then, asks the Gemara - is he lenient in our Mishnah by Eruv (Techumin), which (the Gemara currently believes) is also d'Oraysa?

(b)Not so! answers the Gemara - Rebbi Meir holds that Eruvei Techumin is de'Rabbanan, in which case, his two statements are consistent.

(c)The size rope used for measuring the Techum Shabbos was fifty Amos.

8)

(a)'Yachol Lehavli'o' - means that, if the people who were measuring the Techum Shabbos encountered a ravine, then, provided from edge to edge measured less than fifty Amos, they would use the regular rope, and ignore the slope, by one person standing at one edge holding one end of the rope, and the other, standing at the other edge holding the other end.

(b)'Shamati she'Mekadrin he'Harim' - means that, if the fifty Amos is too short to cover the gap, then they would use a small rope of four Amos, and stretching it taut, the man who stood below would hold one its one end by his heart, and the other man (the one standing above), would hold the other end by his feet (this would ensure that the rope remained at an angle of a hundred and eighty degrees, thereby avoiding the increase in distance caused by the slope.

(c)When measuring the Techum of an Ir Miklat or the distance between two towns with regard to an Eglah Arufah - they would measure the distance as it was, neither 'be'Havla'ah' nor by means of 'Mekadrin be'Harim'.

(d)Rebbi Meir himself holds that Techumin d'Oraysa. When he issued the ruling of 'Mekadrin be'Harim', he was quoting Rebbi Dusta'i b'Rebbi Yana'i, who holds Techumin de'Rabbanan, but he himself did not agree with that.

9)

(a)The Chachamim rule that someone who touched a Safek Chai, Safek Mes during the night, and in the morning he is found to be dead, is Tamei - because 'by all Tum'os, we go after how they are found (i.e. since they found the corpse dead, we assume that it was dead when the person touched it).

(b)Rebbi Meir holds that he is Tahor - because he has a Chezkas Chai, and we say that he only just died. This appears to clash with Rebbi Meir in our Mishnah, who holds Sefeika d'Oraysa Lechumra, and declines to place the Eruv on a Chazakah (to say that it only became Tamei after Shabbos).

(c)If Rebbi Meir would really go after the Chazakah to be lenient even by a Safek d'Oraysa, and our Mishnah would speak when there was a Sheretz on the Eruv during the entire Bein Hashemashos, so that there is no Chazakah - then we would need to understand on what grounds Rebbi Yossi rules there 'Safek Eruv Kasher.

(d)Rabah and Rav Yosef establish our Mishnah by two pairs of witnesses - meaning that Rebbi Meir is strict in our Mishnah, because there, there is at least one pair of witnesses who testify against the Chazakah, thereby negating it (whereas in the Mishnah in Taharos, where this is not the case, there is no reason (according to Rebbi Meir), not to go after the Chazakah. Whereas Rebbi Yossi in our Mishnah, we ignore the pair of witnesses (due to the fact that there is a second pair who clash with them), and place the Eruv on a Chazakah.

10)

(a)According to Rava, the reason that Rebbi Meir takes a more lenient view in the Mishnah in Taharos - is because there are two Chazakos there, not just one, as is the case in our Mishnah: i.e. the Chezkas Chai of the dead person, and the Chezkas Tahor of the person who touched it.