1)

(a)According to Beis Shamai, when Yom-Tov falls on Shabbos, the Amidah comprises eight Berachos - the opening three, the closing three (that one recites by every Tefilah), and two in the middle, one for Shabbos and one for Yom-Tov.

(b)According to Beis Hillel, one recites only seven Berachos. In their opinion, the middle Berachah is the regular one for Shabbos, only one mentions Yom-Tov in the middle of it. Rebbi says - that one also concludes 'Mekadesh Yisrael v'ha'Zemanim'.

(c)When that Beraisa-expert cited the end of the Berachah as 'Mekadesh Yisrael, v'ha'Shabbos v'ha'Zemanim' - Ravina pointed out that this implied that it was Yisrael who sanctified the Shabbos. But that is incorrect, since Shabbos has been automatically sanctified since the creation. Consequently, he must amend the text to the wording of Rebbi (in b.).

2)

(a)When Rosh Chodesh and Chol ha'Mo'ed fall on Shabbos, one acknowledges them in the Amidah, according to the Tana Kama of the Beraisa, by inserting them in the Avodah ('Retzei'), like Ya'aleh v'Yavo. According to Rebbi Eliezer - one inserts them in 'Modim', like 'Al ha'Nisim'.

(b)Someone who forgot to insert them - needs to repeat the Amidah.

(c)At Musaf, according to the Tana Kama, the middle Berachah is that of Shabbos, only one adds Yom-Tov in the middle. This opinion however, is not Halachah - because we also insert Yom-Tov into the conclusion, like the opinion of Rebbi in 1b.

(d)Nor is the Halachah like Raban Shimon ben Gamliel and Rebbi Yishmael Bno shel Rebbi Yochanan ben Berokah - who say that we insert Yom-Tov into the middle of the middle Berachah by all Tefilos (rather than 'Ya'aleh v'Yavo' in 'Retzei').

3)

(a)Rebbi Chiya bar Ashi Amar Rav permits placing an Eruv Techumin with a condition (that it is not Yom-Tov), on the first day of Yom-Tov (when there are two days); Rava permits only the preparing of an Eruv Tavshilin then. The practical difference with regard to preparing these two Eruvin on the first day of Yom-Tov) is, that - whereas one must place the Eruv Techumin again on the second day of Yom-Tov (since one needs to prepare the Eruv in order to be able to leave the Techum on Shabbos, whether it is Yom-Tov or whether it is week-day), it is not necessary to prepare the Eruv Tavshilin again (because should the second day be a weekday, no Eruv is necessary; and if the second day is Yom-Tov, then the Eruv that they prepared on the first day was valid anyway).

(b)Rava does not agree with Rav. In his opinion, Chazal did not permit being 'Koneh Shevisah' (acquiring one's place) on Shabbos. Making an Eruv Tavshilin on the other hand, is permitted, because it does not entail any Isur, and it is only because of Kavod Shabbos (as Rava said above on 15b), that Chazal required an Eruv Tavshilin.

(c)The Tana Kama permits filling a pot-full of meat (to cook) or (to carry) a barrel-full of water, even if it is more than one's needs, but forbids placing more loaves in the oven to bake than are needed - because, whereas the first two cases are all achieved with the same one act, each loaf that one places in the oven is a separate act.

(d)But Rava rules like Rebbi Shimon ben Elazar - who permits filling the oven with loaves, even if one does not require them all, because, he maintains, the loaves bake better when the oven is full.

4)

(a)The Gemara asks whether, if someone forgot to prepare an Eruv Tavshilin, his flour is forbidden - because, if it is, then before anyone else will be permitted to cook or to bake for him, he will have to give them his food or his flour (with a proper Kinyan) - See Tosfos DH 'I Amrat', who learns the opposite.

(b)The Halachah is that his flour is indeed forbidden (as we learn from a Beraisa).

(c)If someone forgot to prepare an Eruv Tavshilin ...

1. ... the Beraisa forbids him to cook, bake - and wrap the food to preserve its heat (Hatmanah).

2. ... he may not cook etc. for others.

3. ... others may not cook for him unless he gives them his flour (as we just explained).

5)

(a)The Gemara also asks whether if someone who forgot to prepare an Eruv, did cook, he is permitted to eat the food that he cooked. We try to bring a proof that he is not, from the Beraisa, which presents the concession of giving one's flour to someone else to bake for him, but not the case of someone who went ahead and baked despite the prohibition. We conclude however, that there is no proof from there - since the Tana may well only be speaking about Takanos that are permitted, and not those that are forbidden.

(b)Another Beraisa specifically forbids someone who cheats and cooks, to eat what he cooked - meaning that, after he has eaten, he decides that he needs more food for guests (although he does not really expect any) So he cooks again on their behalf.

(c)We have no proof from here either that someone who transgressed and cooked, is forbidden to eat the food - since Chazal may have been more stringent by someone who cheats, than someone who transgresses openly, because nobody will learn from the latter (as they will from the former), and, in addition, he too, will realize that he has done wrong and will do Teshuvah (whereas the person who cheats will not).

(d)The difference between this case of cheating and the case that we learned earlier on 11b, where Rav Ada bar Ahavah cheated and salted the pieces of meat of an animal that had been Shechted on Yom-Tov - is that here there is an Isur of cooking on Yom-Tov involved), whereas with Rav Ada bar Ahavah we have a principle 'Ein Ibud b'Ochlin' (the Isur of tanning the meat does not apply to food). So what is the problem, Tircha? If that is the only Isur involved, the fact that if he is not permitted to salt all the pieces might cause him not to Shecht the animal in the first place, and Simchas Yom-Tov overrides Tircha.

6)

(a)The Beraisa explicitly permits eating the Eruv before having used it.

7)

(a)Rav Nachman bar Yitzchak establishes the Beraisa which forbids someone who cheated and cooked, to eat what he cooked, like Beis Shamai according to Chananya - who says that one may only bake on Yom-Tov for Shabbos if one prepared bread for one's Eruv, cook if one prepared a cooked dish and wrap if one prepared something wrapped, making him a likely candidate for the stringent ruling of the Beraisa of cheating.

(b)The Beraisa which permits fruit that was Ma'asered on Shabbos b'Shogeg, but forbids it if it was Ma'asered b'Meizid, is also no proof that if someone cooked without an Eruv, his food is forbidden - because that Beraisa may be speaking when he had other fruit, so that the Ma'asered fruit was not crucial to his Simchas Yom-Tov.

(c)We reject the proof from a similar Beraisa, which forbids vessels that were Toveled on Shabbos on purpose, in two ways. One of them, in exactly the same way as we dealt with the previous proof from someone who Ma'asered - the other grounds for rejecting the proof is that even if he has no other fruit, his Ma'asered fruit is forbidden, because he has the option of borrowing, whereas someone who failed to prepare an Eruv cannot.

(d)We reject the proof from the Beraisa which forbids food that one cooked deliberately on Shabbos - because there he performed a Melachah which is Asur d'Oraisa (cooking), whereas cooking on Yom-Tov for Shabbos (with which we are concerned) is only an Isur d'Rabanan, and may well be permitted if one transgressed and did it.

8)

(a)According to the Tana of our Mishnah, Beis Shamai and Beis Hillel argue over whether one dish will suffice for Eruv Tavshilin, or whether two dishes are required. According to Rebbi Shimon ben Elazar - they both agree that Eruv Tavshilin requires two dishes; what they are disputing is whether a fish with the egg with which it was smeared before cooking is considered one dish or two dishes.

(b)Beis Shamai agree with Beis Hillel that if one cut up an egg and placed it or minced leak inside a fish, they are considered two dishes.

(c)The Halachah is like our Tana in Beis Hillel - that one dish cooked will suffice for Eruv Tavshilin (see Tosfos DH 'Amar Rava' - that that is as far as cooking is concerned, but that, for baking, one requires a loaf of bread too).

(d)Abaye says that if someone had already begun to knead his dough when his Eruv was eaten or lost - he is permitted to finish the dough that he begun.

9)

(a)If Yom-Tov falls on a Sunday - one must Tovel one's Tamei utensils for Yom-Tov the latest on Friday (because it is forbidden to Tovel vessels on Shabbos).

(b)We learn from the Pasuk "u've'Nivlasam Lo Siga'u" - that one is obligated to be Tahor for Yom-Tov.

(c)If someone wishes to fulfill this obligation, if Yom-Tov falls on Sunday, he must Tovel for Yom-Tov ...

1. ... on Friday, according to Beis Shamai - because a man too, may not Tovel on Shabbos or Yom-Tov.

2. ... according to Beis Hillel - on Shabbos, because seeing as this is only a Din in Mar'is ha'Ayin, it is only forbidden when it is obvious what he is doing; which is not the case when a person Tovels, because as far as onlookers are concerned, he may just be entering the water in order to cool down.

10)

(a)'Hashakah' comprises taking Tamei water that is inside a stone vessel and dipping it in a Mikvah until the two waters touch - thereby rendering the water Tahor. This works through the principle of sowing, as if one had sowed the Tamei water in the Tahor water of the Mikvah (and not through Tevilah).

(b)Even Beis Shamai agree that Hashakah is permitted on Shabbos. Hashakah must be performed in a stone vessel - because any other vessel would become Tamei through the contact with the Tamei water, and we have learned that Chazal did not permit Hashakah if the vessel is Tamei as well.