(Mishnah): If a person's head and most of his body were in the Sukah but his table was in the house - Beis Shamai say that it is invalid and Beis Hillel say that it is valid.

Beis Hillel to Beis Shamai: Once, the Elders of Beis Shamai and Beis Hillel visited Yochanan ben HaChoroni (on Sukos) and found him sitting with his head and most of his body inside the Sukah and his table inside the house (and they did not object).

Beis Shamai respond: This is not a proof, as they in fact said to him, "If you have always behaved this way, you have never performed the Mitzvah of Sukah".

(Gemara): Even if his table is not actually inside his house, but he is sitting in the Sukah and there is an open space in his house in front of him which is the size of his table, Beis Shamai say that it is invalid (as he might move into the house).

Question: How long is 'the size of his table'? A Tefach.

R. Yuda bar Pazi and R. Aiyvu bar Nagri were sitting, and they said - we have learned in a Mishnah (in Maseches Terumos; "Beis Shamai and Beis Hillel disagree when a Se'ah of Tameh Terumah fell into 100 Se'ah of Tahor Terumah, Beis Shamai prohibit it and Beis Hillel permit it...After they agreed, R. Eliezer said ....etc.") Who agreed to whom? Did Beis Shamai agree to Beis Hillel or vice-versa?

They said - Let's go outside (of the Beis Midrash) and learn the answer from the Amoraim who are not here.

They went outside and heard R. Chizkiyah quoting R. Acha quoting R. Yuda ben Levi as saying - this is the only case in which we find Beis Shamai (retracting and) agreeing to Beis Hillel.

R. Chuna quoting Rav Avya: There is a Beraisa that teaches this -

One who was pouring Terumah from vessel to vessel and a Tevul Yom touched the stream (only the stream is Tameh. This is a case of Tameh Terumah mixing with Tahor Terumah), it will be permitted if there are 101 parts Tahor to 1 part Tameh.

Proof: If you say that Beis Hillel agreed to Beis Shamai (in (f)) that the Tameh Terumah is not annulled and the mixture is prohibited), who is the Tana here who says that the Tameh Terumah is permitted - it is neither Beis Hillel nor Beis Shamai! (This therefore proves that Beis Shamai agreed to Beis Hillel.)

Rebuttal (R. Idi): We could say that Beis Hillel taught it before they retracted!

Proof (R. Yosa): No, the Mishnah (in Terumos) itself proves that Beis Shamai agreed to Beis Hillel - "After they agreed, R. Eliezer said Terumah should be separated and burned". Was R. Eliezer not a student of Beis Shamai, and he said that one should separate Terumah! (This proves that Beis Shamai agreed to Beis Hillel, as Beis Shamai originally would have held that it must all be burned.)

Proof #2 (R. Chinana): It is clear from the Mishnah that B"S agreed to B"H, as if it were the opposite, the Mishnah could not have continued with the dispute between R. Eliezer and the Chachamim! (Note: This entry and those that follow are according to the explanation of Rav Chaim Kanievski.)

Question: But surely B"S questioned B"H and there was no response! (This seems to prove that B"H agreed to B"S!)

Answer (R. Avun): B"H has a different reasoning from that which is mentioned in the Mishnah, as the Beraisa of R. Hoshiya teaches -

If Terumah Tehorah (which is stringent) and is punishable with death from heaven if a non-Kohen eats it, can become annulled in the mixture; Terumah Temeyah which involves the 'mere' negation of a positive Mitzvah if a Kohen eats it, certainly will become annulled and permitted.

Question: In what merit did Beis Hilel have the Halachah established like them?

Answer (R. Yehuda bar Pazi): In relating a dispute with Beis Shamai, they would first express the opinion of Beis Shamai and there were occasions when they actually retracted and agreed with Beis Shamai.

Question: How do you know that B"H would first express the opinion of B"S? Perhaps it was the Tana who related the opinion of B"S before B"H since they were older, as we find in the story earlier (28-1 (b))?

Answer: If that was so, the discussion would have been related in 2nd person (our Elders and your Elders) not 3rd person (the Elders of Shamai and Hilel).

R. Zeira/ Rav Huna quoting Rav: (In our Mishnah) the Halachah follows Beis Shamai.

R.Yirmiyah/ R. Shmuel bar Rav Yitschak quoting Rav: From the fact that Beis Shamai questioned B"H in the Mishnah without a response, this shows that the Halachah follows Beis Shamai.

(Mishnah): Women, slaves and children are exempt from Sukah.

A child that does not need his mother is obligated in Sukah.

There was story of the daughter-in-law of Shamai the Elder who gave birth; Shamai removed the roofing over the baby's crib and laid Schach for the baby.

(Gemara - Question): Who is considered a child (that is exempt)?

Answer #1 (House of Yanai): A child who needs his mother to wipe him (when he relieves himself).

Answer #2 (R. Yochanan): A child who wakes up and calls for his mother.

Beraisa (R. Hoshiya): A child who does not need his mother is obligated in Sukah and may accompany his mother using the Eiruv that she made for herself.