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1)

(a) If two brothers marry two orphan sisters, one of them a Ketanah who was married off by her mother or brother, and then the brother (the husband of the older sister), dies; the Zikah (his ties with the Yevamah), forbids him to remain with the younger sister - whose marriage is only mi'de'Rabbanan. On the other hand, his marriage to the younger sister prevents him from making Yibum with his Yevamah.
So Rebbi Eliezer says that we instruct the younger sister to make Miy'un (to walk out of the marriage and to nullify it retroactively).

(b) Rebbi Eliezer says that, even if someone bakes small individual doughs which, in themselves, are too small to be Chayav Chalah, the moment he combines them in one basket, they become Chayav Chalah.

(c) Shmuel rules like both of these Mishnahs, despite the fact that the author in both cases is Rebbi Eliezer, who is a Shamuti - and even though these Mishnahs are not in Taharos, like the previous four.
The proof from the second Mishnah (that Shmuel follows Rebbi Eliezer's opinion even in the rest of Shas) is a better one, because Rebbi Eliezer in the first Mishnah, is not an individual opinion (at first we thought that Rebbi Elazar (ben Shamua) holds like him, but finally, we conclude that it is Rebbi Yehudah ben Bava).

(d) If Rebbi Yehudah ben Bava (in the case of 'Mema'anin es ha'Ketanos') would have meant the Ketanos of the world, then, in the following case, he should have said 've'she'Masi'in es *ha'Nashim*' (in the plural). But now that he says 've'she'Masi'in es *ha'Ishah*' (in the singular), we see that Rebbi Yehudah does not refer to the women or the Ketanos of the world, so he must have meant the two cases - of Rebbi Eliezer and of Rebbi Elazar.

(a) If Shevi'is applies to a species of tree, it means the owner is obligated to render it Hefker, and is forbidden to do business with its fruit.

(b) No! it is not obvious that wherever Shemitah applies, the Din of Biy'ur applies too. Because any species which remains in the fields throughout the duration of winter (which is clearly subject to the Dinim of Shemitah), is not subject to Biy'ur.

(c) If not for the Mishnah, we might have said that the produce of the trees mentioned there, are not called fruit - like the sap of the Kataf tree, which will be discussed later in the Sugya.

(a) Rebbi Pedas said that the author of the Mishnah in Shevi'is is Rebbi Eliezer, because Rebbi Eliezer is the Tana who holds that sap is called a fruit, and that therefore the Kataf tree is subject to the Dinim of Shemitah.

(b) What Rebbi Zeira meant was, that from the statement of Rebbi Pedas in the previous answer, in conjunction with the statement of Rebbi Elazar, Rebbi Pedas' father, who rules like Rebbi Eliezer in only four cases - from which we can deduce that, in all other cases, the Halachah is not like him. Consequently, the Kataf tree will be permitted in the Shemitah.

(c) The Gemara proves from here that, that when Rebbi Elazar ruled like Rebbi Eliezer on four occasions, he was referring to the whole of Shas, and not just to Seider Taharos (otherwise, why did Rebbi Pedas not answer that his father's statement was restricted to Taharos).

(a) Rebbi Elazar rules like Rebbi Eliezer by 'Melamdin es ha'Ketanah', even though it is not in Seider Taharos, because Rebbi Yehudah ben Bava holds like him.

(b) He also rules like Rebbi Eliezer with regard to saying Havdalah in the Amidah on Motzei Shabbos in the Berachah of Modim, because there too, Rebbi Eliezer is not an individual opinion - since Rebbi Chanina ben Gamliel holds like him.

(c) Rebbi Chanina ben Gamliel says that Havdalah on Motza'ei Yom Kipur, like on Motza'ei Shabbos, is said in the Berachah of Modim, in which case it is possible for the Amidah on Motza'ei Yom Kipur to comprise seven Berachos.
He quoted his fathers however, who maintain that it is necessary to recite the full eighteen Berachos on Motzei Yom Kipur, in order to say Havdalah in 'Chonen ha'Da'as' (which incidentally, is the ruling that we follow).

5)

(a) The Rabbanan argue with Rebbi Eliezer by the sap of a tree, which they hold is not considered fruit, whereas the Mishnah in Orlah, which considers sap to be fruit, regarding the Dinim of Orlah, is speaking about the sap of fruit, a distinction which Rebbi Yehoshua explicitly makes there (It appears from here that a Kataf tree *does* produce fruit, whereas from the second answer of the Gemara, it would appear that it does not - see Tosfos ha'Rosh).
Alternatively, the Rabbanan argue with Rebbi Eliezer with regard to a tree which bears fruit, where they say that the sap is insignificant. But, by a tree which produces no fruit, they agree with Rebbi Eliezer that the sap is considered its fruit. (According to this answer, the author of the Mishnah of Kataf can be the Rabbanan just as well as Rebbi Eliezer, not like the opinion of Rebbi Pedas.)

(b) If the Rabbanan who argue with Rebbi Shimon are really Rebbi Eliezer, who considers even sap from a fruit-tree to be fruit, then what they are saying to Rebbi Shimon is 'According to us, all sap is considered fruit, but won't you at least agree with us by a Kataf-tree, where the sap is its fruit?'

(a) As long as a girl of under twelve has not been intimate with a man, she is a Besulah; a Kohen Gadol may marry her, and, if she gets married, her Kesubah is two hundred Zuz.
Ground is considered virgin soil as long as it has not been worked: It is Kasher to be used as a Nachal Eisan, to break the neck of an Eglah Arufah, and, because it is better quality soil, if someone stipulates that he is buying virgin soil, then that is what the seller must give him.
A young 'Shikmah' (a type of wild-fig tree), remains a 'Besulas ha'Shikmah' as long as the bark has not yet been cut: both as regards buying and selling, since the purchaser wants a tree that has not yet been cut, so that after he cuts it the first time, it grows thicker, and as regards cutting it in the Shemitah, which is forbidden.

(b) The Gemara rejects the initial wording of the fourth answer - that the Beraisa only mentions those things on which the purchaser is particular, because the purchaser is equally particular about the blood of a 'Besulas Damim', for so Rebbi Chiya taught in a Beraisa 'Just as yeast is good for dough, so too, is blood good for a woman - and Rebbi Meir said 'the more blood a woman has, the more children she will have.

(c) The new version of this answer is that the Beraisa only deals with cases where being a 'Besulah' is an advantage, but not where, on the contrary, the man is waiting for her virginity to break, to find out whether she has a lot of blood.

(d) The Gemara also answers that the Tana lists only those things where the virginity is broken by an act (i.e. intimacy, digging and cutting), whereas a Besulas Damim loses her virginity through seeing blood - without an act being performed.
All the other 'Besulos' are permanent; i.e. once they have been removed, they will never return. Whereas the Din of 'Dayah Sha'atah' of a Besulas Damim will return when she becomes old.

(a) A woman has the Din of a pregnant woman (regarding the Din of Dayah Sha'atah), only when, besides the obvious sign that she is pregnant, three months have also passed since the time of intimacy (and this will aply even to a sixth or seventh month baby).

(b) The Pasuk of "Vayehi ke'Mishelosh Chodashim" by Tamar is not a proof for this principle, because Tamar might well have given birth in nine months, in which case three months would have constituted a third of her pregnancy (in fact, she gave birth in six, but they could not have known that at the time). Maybe by a woman who gave birth in six months (and a day), it would be called 'Hukar Ubrah' in two months - whereas according to the ruling of the Gemara, it must always be a minimum of three months (because we follow the majority of pregnancies).

(c) A pregnant woman who sees blood and then immediately gives birth to a non-baby, we consider the pregnancy a good pregnancy, and rule 'Dayah Sha'atah'.

(d) There can be no proof from the Pasuk "Hareinu Chalnu, Kemo Yaladnu Ru'ach", which seems to assume that such a birth *is* considered a birth, because the Pasuk is speaking about men, and can therefore be no more than a Mashal - it is a nice hint, but not a proof!

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