1)

(a)Beis Shamai forbids carrying a child, a Lulav or a Sefer-Torah into the street on Yom-Tov - Beis Hillel permit it.

(b)Their Machlokes applies to carrying anything which is not actually Ochel Nefesh.

2)

(a)When that Beraisa expert quoted a Beraisa which sentences someone who Shechts an Olas Nedavah on Yom-Tov to Malkus - Rav Yitzchak bar Avdimi said to him that the author must be Beis Shamai, who does not permit carrying anything which is not for Ochel Nefesh. Beis Hillel would exempt him from Malkus, because - since Shechitah is permitted for a person's own benefit, there can be no Malkus for Shechitah, even by a Shechitah that is itself not permitted (a principle known as 'Mitoch').

(b)According to Rabah, Beis Shamai and Beis Hillel argue over whether Eruv and Hotza'ah apply on Yom-Tov or not - Beis Shamai learn the prohibition of carrying on Yom-Tov from that of Shabbos; whereas according to Beis Hillel, the Isur of carrying is confined to Shabbos, but not to Yom-Tov.

(c)Beis Hillel learn this from the Pasuk "v'Lo Sotzi Masa mi'Bateichem b'Yom ha'Shabbos" - implying that the Isur of carrying is confined to Shabbos, but does not apply to Yom-Tov.

(d)The author of the Beraisa quoted in a. could be Beis Hillel, according to Rabah - because their lenient view in our Mishnah is restricted to carrying, and has nothing to do with other Melachos, which Beis Hillel will not exempt because of 'Mitoch'.

3)

(a)Rav Yosef proves Rabah wrong from the fact that Beis Shamai and Beis Hillel argue by the objects specified in our Mishnah - because, according to Rabah, in whose opinion, Beis Hillel permits carrying outright on Yom-Tov, why do they not argue by stones (since, the Rabbinical decree of Muktzeh is based on the Torah's prohibition of carrying. Consequently, wherever there is no Isur of carrying, there will be no Isur of Muktzeh either). That being the case, since they do not argue by stones, it is clear that one may not carry stones on Yom-Tov (mid'Rabanan) because of Muktzeh, in which case, there must be an intrinsic Isur of carrying.

(b)Even though Beis Hillel permits carrying mi'd'Oraisa, even when it is not necessary (See Tosfos DH 'Hachi Garsinan', who disagrees with this) - nevertheless the Chachamim decreed carrying anything that is not needed, because of unnecessary bother.

4)

(a)A Beraisa expert quoted a Beraisa to Rebbi Yochanan which sentences someone who cooked a Gid ha'Nasheh in milk and ate it, to five sets of Malkus, two for cooking - Gid ha'Nasheh on Yom-Tov and Basar b'Chalav; two for eating - Gid ha'Nasheh and Basar b'Chalav, and one for making a fire - on Yom-Tov.

(b)Rebbi Yochanan suggested that to the Beraisa expert, that, unless he wished to establish the Beraisa like Beis Shamai - he should erase from the Beraisa both Lavin connected with Yom-Tov (making a fire and cooking the Gid ha'Nasheh), for which, according to Beis Hillel, he will not receive Malkus.

(c)We extrapolate from Rebbi Yochanan's statement - that he too, learns like Rav Yosef (that Beis Hillel's reason in our Mishnah is because of 'Mitoch' - and not because of Eruv v'Hotza'ah). That explains why, in his opinion, a person cannot receive Malkus for making a fire or cooking on Yom-Tov (according to Tosfos, provided it has some use on Yom-Tov).

5)

(a)Beis Shamai forbid taking Chalah or Matanos to a Kohen on Yom-Tov - Matanos refers to the right foreleg, the cheeks and the stomach called Keivah, all of which one is obligated to give to the Kohen from every Chulin animal that is Shechted. There is no Isur in eating from an animal from which the Matanos have yet not been given to the Kohen, though one should avoid doing so before the Matanos have been separated.

(b)According to the Tana of our Mishnah, Beis Shamai do not differentiate between Chalah and Matanos that were separated before Yom-Tov and those that were separated on Yom-Tov itself.

(c)Beis Shamai prove their point of view from Terumah - which one may certainly not take to the Kohen on Yom-Tov.

(d)Beis Hillel reject Beis Shamai's proof - on the grounds that Terumah is different, since it can also not be separated on Yom-Tov (whereas Chalah and Matanos can).

6)

(a)According to Rebbi Yehudah - even Beis Shamai agree that Matanos that were Shechted and separated already yesterday may be taken to the Kohen together with those that were separated today and with those that were Shechted today. What Beis Shamai forbids is to take them on their own.

(b)According to Rebbi Yosi, Beis Shamai and Beis Hillel permit carrying Chalah and Matanos, and they only argue by Terumah.

(c)He maintains that it is Beis Hillel who learns the Heter to take Terumah to a Kohen from Chalah and Matanos (rather than Beis Shamai who learns the Isur by Chalah and Matanos from Terumah).

(d)Beis Shamai counters this by arguing - that one is only permitted to carry Chalah and Matanos, since one is permitted to separate them on Yom-Tov, but not Terumah, which one is not.

7)

(a)Acherim holds like the Tana of our Mishnah - that both Beis Shamai and Beis Hillel agree that it is Asur to take Terumah to the Kohen, and that they argue over Chalah and Matanos, which Beis Shamai forbid and Beis Hillel permit.

(b)Our Mishnah, which specifically forbids Terumah according to both Beis Shamai, and which establishes their Machlokes by Chalah and Matanos - cannot possibly go like Rebbi Yosi.

(c)In order to accommodate Rebbi Yehudah's opinion - we establish 'Bein she'Hurmu me'Emesh, Bein she'Hurmu me'ha'Yom' (that Beis Shamai say in our Mishnah with regard to Chalah and Matanos) - to speak when either way, the animal was Shechted yesterday (because had it been Shechted, as well as separated, today, then Beis Shamai would agree that one is permitted to send it to a Kohen).

(d)Rebbi Yehudah is more lenient than Acherim in the point that we just mentioned: namely - that, in Rebbi Yehudah's opinion, Beis Shamai will permit sending Chalah and Matanos to a Kohen if the dough was actually made, or the animal was Shechted, on Yom-Tov; whereas Acherim does not differentiate.

8)

(a)Rav Tuvi brei d'Rav Nechemyah asked Rav Yosef about sending a barrel of Terumah-wine to a Kohen on Yom-Tov. He replied that Rav Yehudah Amar Shmuel had already ruled like Rebbi Yosi in the previous Beraisa, and that it was therefore permitted.

(b)It might be forbidden to roll mustard-pods to obtain the seeds on Yom-Tov - because it is a Toldah of Dishah (threshing), and it was possible to have accomplished it before Yom-Tov.

(c)This is not a straightforward case of 'Ochel Nefesh', which is permitted - because any Melachah which could have been performed yesterday, without in any way, detracting from the quality of the food, is forbidden on Yom-Tov.

(d)When Rava was asked this very question, he ruled leniently - because rolling legumes in this manner is kel'Achar Yad (not the usual way of performing the Melachah), in which case one would not even be Chayav on Shabbos. Consequently, Chazal did not even issue a decree forbidding it on Yom-Tov.

9)

(a)The Beraisa permits someone who rolled soft wheat-grains on Erev Shabbos to blow them on Shabbos 'mi'Yad l'Yad' - meaning to blow them from one hand to another, as this is an unusual way of removing the shells.

(b)The Tana permits someone who rolled wheat-grains on Erev Yom-Tov - to separate the waste from them even using a cone-shaped funnel or a dish, which allow the food to go through, but which hold back the waste, provided he sifts only small amounts at a time.

(c)He forbids however, using a board or a regular sifter or sieve for this purpose.

(d)The reason that the Tana is strict with regard to using these implements - is because people who do use them, usually sift large quantities, not only for Yom-Tov, but also for after Yom-Tov.

10)

(a)The above Beraisa, which appears to permit only wheat-grains that were rolled on Erev Yom-Tov - really permits those that were rolled on Yom-Tov, too. The reason that the Tana mentions exclusively Erev Yom-Tov, is only because of the Reisha, where it speaks about wheat kernels that were rolled on Erev Shabbos (which is definitely Asur on Shabbos itself).

(b)Once the wheat-grains have been rolled, and the outer husks removed - the grain becomes fit to have Terumah separated from them.

(c)The author of our Mishnah, which clearly states that corn can never reach the stage when it becomes Chayav Terumah on Yom-Tov - is Rebbi Yosi b'Rebbi Yehudah, who holds that corn does not reach the stage of Terumah by merely rolling it and removing the outer husk, and it is according to Rebbi, that it does.