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1)

(a) According to the Tana Kama, someone who is Noder from milk, is permitted to eats the whey, and vice-versa (because they are considered two different commodities) - Rebbi Yossi forbids the former.

(b) Aba Shaul says that someone who is Noder from cheese is forbidden to eat both salted and unsalted cheese. We might otherwise have confined the Neder to salted cheese, because that is how cheese is usually made?

(c) The Tana Kama permits someone who is Noder from meat, to eat both the gravy and the Kifah - which is the tiny pieces of meat that one finds at the bottom of the pot.

(d) Rebbi Yehudah forbids both the gravy and the Kifah.

(a) When Rebbi Yehudah cites Rebbi Tarfon, who even forbade eggs that were cooked together with meat that was forbidden through a Neder - he is bringing a proof for Rebbi Yossi, who forbids the whey together with the milk (see also Tosfos).

(b) The Rabbanan refute Rebbi Yehudah's proof - by establishing Rebbi Tarfon when the Noder said 'Basar Zeh', specifically including whatever comes from it (or whatever it is mixed with).

(c) The criterion for Rebbi Tarfon's ruling, according to them is - whether there is sufficient of the forbidden food to give taste to the secondary one (which is generally anything less than sixty to one).

(d) The difference whether one is 'Noder min ha'Yayin' or 'Konem Yayin Zeh she'Eini To'em' is - that in the former case, one is only forbidden to drink the wine itself; whereas in the latter, whatever comes from the wine or whatever it is mixed with and absorbs some of its taste is included in the Neder (like the Rabbanan of Rebbi Yehudah).

(a) The problem that we have with the concession of benefiting from forbidden wine because it is less than a sixtieth - is the principle 'Davar she'Yesh Lo Matirin, Afilu be'Elef La Bateil'. And Neder is a 'Davar she'Yesh Lo Matirin', since it is a Mitzvah to have it annulled.

(b) Some restrict the Isur of 'Davar she'Yesh Lo Matirin' to when the two objects are of the same kind (Min be'Mino), but not to Min be'she'Eino Mino (such as meat and eggs, milk and whey).

(c) The source of this distinction - is the Yerushalmi in this very Perek.

(a) The distinction between 'Min be'Mino' and 'Min be'she'Eino Mino' leaves us with a Kashya on the Rif, however. According to the Rif, the Gemara forbids bread that was baked together with roasted meat to be eaten with Kutach (in spite of the principle 'Reicha La'av Milsa Hi') - because (seeing as it can be eaten with meat) it falls under the category of 'Davar she'Yesh Lo Matirin'.

(b) The Sugya in Beitzah says - that a dough whose owner borrowed water and salt can only be taken to areas that lie within the T'chum of both owners.

(c) Despite the fact that the reason given there is because it is a 'Davar she'Yesh Lo Matirin', there no proof from there for the Rif's ruling (seeing as flour on the one hand, and water and salt on the other, are Min be'she'Eino Mino') - because the fact that one cannot make dough without water and salt, renders them 'Min be'Mino'.

(a) Many commentaries disagree with the Rif (see Tosfos and the Rosh here) on the basis of our Sugya. It is possible however, to reconcile the Rif with our Sugya. According to the Rif - the predominant factor in determining the difference between 'Min be'Mino' and 'Min be'she'Eino Mino', is the difference in Halachah.

(b) Both of them however - are required in order to become Bateil.

(c) 'Min be'she'Eino Mino' overrides 'Davar she'Yesh Lo Matirin' in the case of Nedarim, but not in the case of ...

1. ... bread that was baked together with roasted meat in the oven - because, unlike by Nedarim (which are completely forbidden now, and permitted later), bread that was baked ... can be eaten now too (with meat or Parev dishes).
2. ... dough containing borrowed water and salt - because, like bread that was baked together with roasted meat in the oven, it can be eaten already now (within the T'chum).

(d) In fact, there might be even more reason to be stringent in the first of the two cases than in the second - because, whereas in the latter case, we would be stringent in the equivalent case by 'Min be'Mino' (creating the possibility of being lenient by 'Min be'she'Eino Mino'); in the former case, which does not have an equivalent by 'Min be'Mino', we will not be lenient by 'Min be'she'Eino Mino' either.

(a) They considered a joke, Rav Ashi's ruling in Yevamos that a piece of Chatas that became mixed in a hundred pieces of Chulin is forbidden because it is a 'Davar she'Yesh Lo Matirin') - because as far as Kohanim are concerned, it is always permitted, whereas as far as Yisre'eilim is concerned, it is always forbidden (so how can he refer to it as a 'Davar she'Yesh Lo Matirin'?).

(b) We reconcile this with the Rif's ruling in the case of bread which was baked together with roasted meat in the oven - because in the case in Yevamos, there is no point in being stringent with regard to the Yisrael (not to allow the piece of Chatas to become Bateil), because of the fact that it is permitted to Kohanim; whereas in the case of bread which was baked together with roasted meat in the oven - we will be stringent now regarding everybody because the bread can be eaten now (by the same people) with meat.

7)

(a) According to the Tana Kama of a Beraisa, someone who is Noder from lentils, is forbidden to eat 'Ashishin' (poor quality lentils that can only be eaten when they are fried in honey) - Rebbi Yossi permits it.

(b) There is no contradiction between this Halachah and their ruling in our Mishnah permitting the whey - because whey and milk are completely different commodities, whereas lentils and Ashishin are not.

(c) But if Rebbi Yossi does not consider Ashishin to be lentils - then how much more so should he not consider whey to be milk.

(d) We reconcile the two statements of Rebbi Yossi - by repeating what we said earlier, that in Rebbi Yossi's town, they referred to whey as 'Kuma de'Chelba', whereas they did not refer to Ashishin as lentils (since they have been changed from what they originally were by having honey added to them).

(a) A Neder forbidding ...

1. ... milk - does not incorporate whey, nor vice-versa.
2. ... gravy - does not incorporate Kifa, nor vice-versa.
3. ... grapes - do not incorporate wine.
4. ... olives do not incorporate oil.

(b) 'Konem Zeisim va'Anavim Eilu she'Eini To'em, Asur Bahen u'Vayotzei Bahen'. The two possible reasons for this are - either because he added the word 'Eilu', or because he added 'she'Eini To'em'.

(c) We ask that if 'Eilu' was Dafka, then why would the Tana need to mention 'she'Eini To'em'? We could just as well have asked the other way round - but chose to ask this way because 'Eilu' appears first in the Mishnah.

(d) We answer - that the Tana mentions 'she'Eini To'em' to teach us that even though he added that, it will not incorporate other foods, unless he said 'Eilu'.

(a) In spite of the Mishnah later, which forbids Chilufin and Gidulin when the Noder said 'Eilu', but not when he said 'she'Eini To'em', Rami bar Chama suggests that 'she'Eini To'em' might be stronger than 'Eilu' - because that Mishnah speaks specifically about Chilufin and Gidulin, which are included only because 'Eilu' is considered as if he had declared the fruit Hekdesh, where Chilufin and Gidulin are forbidden too; whereas 'she'Eini To'em' (which does not have such connotations), if anything precludes Chilufin and Gidulin, seeing as that is not what he forbade.

(b) In another Beraisa, the Tana says 'Konem Peiros ha'Eilu Alai ... Asur be'Chilufeihen u've'Giduleihen' - from which we might infer that what comes from the fruit is permitted (otherwise the Tana should rather have said 'Asur be'Yotze Meihen', which is a bigger Chidush, because it is not the same object as the one that he forbade.

(c) In fact, there is no proof from there that 'Eilu' does not include what comes from the fruit - because we can say the opposite: that Chilufin and Gidulin is a bigger Chidush, seeing as it did not come from the original object (and that in fact, whatever comes from the forbidden object is certainly forbidden).

(d) We could have resolved our She'eilah from the Beraisa, which says 've'Im Amar Basar Zeh Alai, Asur Bo u've'Rotvo u've'Kifo'. We did not do so - because we are looking to resolve it from a Mishnah.

(a) We cannot resolve the She'eilah from the Seifa 'she'Eini Ochel, ve'she'Eini To'em Mutar be'Chilufeihen ve'Giduleihen', from which we can infer 'Ha ba'Yotzei Meihen, Asur' - because we can say that really, 'ba'Yotzei Meihen, Mutar. However, since the Tana did not mention in the Reisha that 'ba'Yotzei Meihen, Asur' (like Chilufin ve'Gidulin), he did not mentions it in the Seifa either.

(b) We finally conclude from Rebbi Yehudah (quoting Rebbi Tarfon) in our Mishnah (who forbade eggs that were cooked with the forbidden meat when the Noder said 'Konem Basar Zeh' (which is like 'Eilu') Alai' - that Eilu is Dafka, and that it includes whatever comes out of the fruit or receives taste from it.

(c) We try to resolve the second half of the She'eilah from the Mishnah that we learned earlier 'Dag Dagim she'Eini To'em Asur Bahen ... *u'Mutar bi'T'ris T'rufah u'be'Tzir'*. Rava refutes the proof from there however - by establishing the Mishnah when the juice had already been extracted and the fish chopped, before he made the Neder (but if it was done only afterwards, it would indeed be forbidden.

(d) The Halachah is that ...

1. ... 'Eilu' - is definitely Dafka.
   
2. ... 'she'Eini To'em' - is a Safek, and S'feika d'Oraysa le'Chumra.

(a) The case of 'she'Eini Ochel' presents a problem - because what alternative did he have? 'Konem Alai' would have implied an Isur Hana'ah, and not just the Isur Achilah that he wanted to create.

(b) We resolve this problem - by pointing out that he could have said 'Konem Peiros ha'Eilu ba'Achilah', rather than 'Konem Peiros she'Eini Ochel'.

(c) In that case, by She'vu'ah, 'she'Eini Ochel' will definitely not include anything (e.g. what comes from the fruit) - because 'ba'Achilah Alai' is not an alternative, seeing as it is a Lashon of Neder and not of Shevu'ah, in which case 'she'Eini Ochel' is not superfluous.

(d) The Rambam says otherwise - because, in his opinion, the Leshonos under discussion do not include because they superfluous, but because the Lashon itself is inclusive. In that case, there is no difference between Neder and Shevu'ah.