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1)

(a) Beis Shamai invalidates an old Sukah - according to Beis Hillel, an old Sukah is Kasher.

(b) An old Sukah is one that was built more than thirty days before Sukos (when we assume that the builder did not have the Mitzvah in mind).

(c) Even Beis Shamai concedes that an old Sukah is Kasher if the owner had the Mitzvah in mind at the time when he built it.

(a) Beis Shamai learn the Pesul of an old Sukah from the Pasuk "Chag ha'Sukos ... Shiv'as Yamim la'Hashem" - implying that the Sukah must be built 'Lishemah' (for the sake of Hashem - i.e. for the Mitzvah).

(b) Beis Hillel learn from this Pasuk the Derashah of Rav Sheshes quoting Rebbi Akiva - who learns from there that the wood of the Sukah is designated for Hashem (i.e. forbidden throughout Sukos).

(c) Rebbi Yehudah ben Beseira learns this from the word "Chag" - which teaches us that a certain Kedushah descends on the wood of the Sukah, just like it does on a Korban Chagigah to forbid its flesh to be eaten until after the fat-pieces have been brought on the Mizbe'ach.

(d) In fact, Beis Shamai too, needs this Pasuk for the Derashah of Rav Sheshes - and he learns the Pesul of Sukah Yeshanah from the Pasuk in Re'ei "Chag ha'Sukos Ta'aseh ... " - implying that the Sukah should be made 'Lishemah' (as if the words were inverted to read "Sukos Ta'aseh le'Chag").

(a) Beis Hillel learn from the Pasuk "Chag ha'Sukos Ta'aseh ... " - that constructing a Sukah on Chol ha'Mo'ed is permitted.

(b) Beis Shamai agrees with Rebbi Eliezer, who forbids constructing a Sukah on Chol ha'Mo'ed.

(a) Rav Yehudah Amar Rav permits balls of thread to be used as Tzitzis - since they were attached to the garment for the sake of the Mitzvah. He does not however, permit fringes, loose threads from woven or stitched garments that were not attached to the garment 'Lishmah'.

(b) He learns this from the Pasuk in Ki Seitzei "Gedilim Ta'aseh *Lach*". Nevertheless, he says, Beis Hillel will not learn from "Chag ha'Sukos Ta'aseh *Lecha*" that a Sukah too, must be constructed 'Lishemah' - because they need that Pasuk to teach us that a stolen Sukah is Pasuk.

(c) "Gedilim Ta'aseh *Lach*" is not needed to disqualify stolen material from being used as Tzitzis - because for that, we have another Pasuk in Sh'lach Lecha "ve'Asu *Lahem* Tzitzis" - 'Lahem mi'she'Lahem'.

5)

(a) A Sukah that is built ...

1. ... underneath a tree - is Pasul as if it had been built inside a house.
2. ... underneath another Sukah - is Pasul, according to the Tana Kama.

(b) In Rebbi Yehudah's opiniion, it is Kasher- if there is no-one living in the top Sukah (and this will be explained later).

(a) the Tana of our Mishnah needs to say that if someone constructs his Sukah underneath a tree, it is *as if he has constructed it inside his house* - to teach us that the tree (which invalidates the Sukah because of one Sukah underneath another), only invalidates it, if, like a house, it casts more shade than sunlight.

(b) We learn from the Pasuk in Re'ei (which is describing the S'chach) "be'Ospecha, mi'Gornecha u'mi'Yikvecha" - that the S'chach must be detached.

(c) A Sukah that is built underneath a tree whose sun is more than its shade is Kasher - only if one is Mevatel the branches of the tree to the S'chach.

(d) 'be'she'Chavtan' means - that one lowers the branches on to the S'chach, until they become indistinguishable from those of the Sukah. Then they become Batel to the S'chach.

(a) The Tana of our Mishnah nevertheless considers it necessary to teach us the previous Chidush. It is not so obvious that, if there is more shade than sun (as Rava pointed out) and the part that is Pasul is Batel (as Rav Papa explained), the Sukah is Kasher - because the Rabbanan might well have decreed even a tree whose sun is more than its shade, because of a tree whose shade is more than its sun, when Bitul does not apply.

(b) If not for the Tana of our Mishnah, we would have thought that the Mishnah later, which teaches us that if one bent a vine, a pumpkin or a kind of creeper over his Sukah (which let in more sun than shade), his Sukah is Kasher - means Bedi'eved, but that, Lechatchilah, one should not do this.

(a) In spite of the plural ("ba'Sukos"), we cannot infer from the Pasuk that one Sukah underneath the other, is Kasher - because, as we saw earlier, "ba'Sukos" is spelt without a 'Vav', implying the singular.

(b) However, the above Halachah (that one Sukah underneath another is Pasul) is not so clear-cut, since all combinations are possible: Both Sukos are Kasher if the bottom one allows in more sun than shade, and the top one is within twenty Amos from the ground; and both Sukos are Pasul - if they both shed more shade than sunlight, and the top one is higher than twenty Amos.

(a) The bottom Sukah is Kasher and the top one Pasul, if the bottom Sukah casts more shade than sun, and the top one, which allows in more sun than shade, is within twenty Amos of the ground. The bottom Sukah is Pasul - if the S'chach of the top one is higher than twenty Amos from the ground - because then it becomes S'chach Pasul, which invalidates the bottom Sukah whenever it is not Batel to it, as we learnt above.

(b) The top Sukah is Kasher and the bottom one Pasul - if both Sukos cast more shade than sun, and the top Sukah is within Twenty Amos of the bottom one.