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1)

(a) The reason that the generation of Rav Yehudah witnessed more miracles than that of Rav Papa cannot possibly have been due to their superior Torah knowledge. Why not?
Because whereas Rav Yehudah's generation generally restricted their learning to Nezikin, in Rav Papa's time, they would learn all six Sedarim. And in addition, Rav Yehudah was flummoxed by Mishnahs in Uktzin, whereas in Rav Papa's days, there were thirteen Yeshivos learning Uktzin.

(b) The reason that Rav Yehudah's generation merited more miracles was because of their acts of Mesiras Nefesh (self-sacrifice) for the sanctification of Hashem's Name, which was lacking in later generations? What did they do? Like the story of Rav Ada bar Ahavah, who once pulled off a red, flashy cloak from the back of a Kutis, whom he took to be a Jewess.

(c) Rav Papa complained because they would pray and pray and pray for rain, but nothing would happen.
Whereas all Rav Yehudah had to do was remove one shoe (as a sign of pain - like we do on Tish'ah be'Av), and the rain would come.

(d) Rav Ada Bar Ahavah soon discovered that the woman was a Kutis, when he was made to pay four hundred Zuz for embarrassing her. When the woman told him that her name was Masun (which means two hundred), he exclaimed ruefully 'Masun Masun (two hundred and two hundred) is worth four hundred (Zuz)'.

3)

(a) Rav Gidal was not afraid that he might sin through watching the women Toveling, because he felt not the least emotionally involved - he considered as ducks.

(b) Rebbi Yochanan used to sit by the gates of Tevilah because he was exceptionally good-looking, and he hoped that the women would see him as they entered, with the result that they would later conceive children as good looking as he (reminiscent of Ya'akov and the spotted and speckled sticks)
The Gemara, incidentally, does not ask (like it asked by Rav Gidal) why Rebbi Yochanan was not afraid of sinning, because Rebbi Yochanan constantly kept his eyes shut, and never looked outside his four Amos (as the Gemara writes at the end of Bava Kama), so that the possibility of sinning was was non-existent, as far as he was concerned.

(c) Rebbi Yochanan was not afraid of Ayin ha'Ra, because he was a descendent of Yosef ha'Tzadik, whose children are not subject to Ayin ha'Ra.

(a) 1. "Ben Poras, Alei Ayin" means a fruitful son (or a son with Chein), who is above the eye - meaning that Ayin ha'Ra cannot affect him. 2. "ve'Yidgu la'Rov" etc., means that they (Yosef's children) will increase like fish ("ve'Yidgu" from the word 'Dag'). Just like fish are covered by water, and are therefore not subject to the Ayin ha'Ra, so too, are Yosef's descendants immune to the Ayin ha'Ra.

(b) The third reason is a more personal one. Namely, that Yosef merited this immunity because he did not derive pleasure from Potifar's wife, who was forbidden to him (presumably by keeping his eyes away from her), he was granted the power to remain unaffected by an Ayin ha'Ra.

(a) Slaves are exempt from those Mitzvos which are time-bound (in the same way as women are); consequently, they are Patur from reciting the Shema (which is recited morning and evening) and from Tefilin (which are not worn on Shabbos).

(b) Children are Patur from the Shema, because, Rashi maintains, the Mitzvah of Chinuch is incumbent upon the father (not upon the child), and the father is not always present when the time arrives to recite the Shema (Rashi therefore learns that even a child who has reached the age of Chinuch is Patur - See Tosfos d.h. 'u'Ketanim').

(c) We would have thought that women, slaves and children are Patur from Tefilah, because it is time-bound (since the Torah writes - in Tehilim), with regard to Tefilah "Erev, va'Voker ve'Tzaharayim".

(d) The reason that Chazal obligated them are to Daven, is because everyone needs Hashem's mercy.

6)

(a) We would have thought that women etc., should be Chayav to recite the Shema, since they too, need to accept upon themselves Malchus Shamayim.

(b) We would also have thought that women and slaves should be Chayav to put on Tefilin, since Tefilin is compared to Mezuzah, which they are definitely Chayav.

(c) We might, on the other hand, have thought, that they are Patur from Mezuzah, because it is placed in juxtaposition to Torah-study, from which they are Patur, since the Torah writes "ve'Limadtem Osam es *Beneichem*" - "Beneichem", ve'Lo Benoseichem'.

(d) Bensching may not be per se time-bound. However, the Torah does write with regard to the Man and the quails: "When Hashem gives you in the evening meat to eat, and bread in the morning to be satisfied" - adding an aspect of time to our eating habits.

(a) Women 's obligation to recite Kidush cannot be no more than a Rabbinical one; because first of all, Rav Ada bar Ahavah said explicitly 'Devar Torah'. And secondly, why should the Rabbanan obligate women to recite Kidush more than any other Mitzvah?

(b) Women are Chayav, because the Torah compares "Zachor" (the positive Mitzvah of making Kidush) to "Shamor" (the negative Mitzvah of not performing Melachos on Shabos) - since we have a tradition that both were said by Hashem simultaneously.

(a) If women are Chayav to Bensch min ha'Torah, then they will be able to be Motzi men with their obligation, but not if their obligation is only mi'de'Rabbanan, because a Rabbinical obligation cannot render Yotze someone whose obligation is min ha'Torah.

(b) Their obligation might not be Torah-oriented, either because they do not initially inherit a part of Eretz Yisrael (Rashi), and the Torah writes "Al ha'Aretz ha'Tovah Asher Nasan Lach".
Or because the mention of B'ris and Torah-study are an intrinsic part of Bensching, as the Gemara will teach us later (49a), and women are Chayav neither B'ris nor Torah-study (see Tosfos d.h. 'Nashim').

(c) A wife may Bensch for her husband - even if her obligation is only mi'de'Rabbanan - (in the same way as a child may Bensch for his father - and in the same circumstances), only if she ate a Shiur d'Oraysa (i.e. enough to be satisfied, whilst her husband only ate a Shiur de'Rabbanan. In that case, the obligations of each of them is only de'Rabbanan, and she can then be Motzi her husband (and a child his father).

(a) "Asher Lo Yisa Fanim" refers to the non-Jews, who do not merit Hashem's favors. Whereas "Yisa Hashem Panav Eilecha" refers to Yisrael (See also Tosfos, Nidah, 70b d.h. 'Kahn').

(b) 'Ad Kezayis' foolows the opinion of Rebbi Meir, who maintains that the Chiyuv de'Rabbanan to Bensch is effective on a Kezayis; 'Ad Kebeitzah' that of Rebbi Yehudah, who holds that one does not Bensch on a Kezayis.

(a) Ezra made a Takanah that a Ba'al Keri should not study Torah (or to Daven) before he has Toveled.

(b) Chazal did not obligate a Ba'al Keri to think the Berachos of the Shema or those before eating, because they are only de'Rabbanan.

(c) According to Rebbi Yehudah, one recites all the Berachos. His reason will be explained later.

(a) Although Hirhur ke'Dibur, it is nevertheless forbidden to recite the Shema aloud, like we find at Sinai, when Yisrael were required to Tovel in order to hear Torah from Hashem, which, on account of the principle 'Shomei'a ke'Oneh' was considered as if they had said it themselves.

(b) Even though one is not Yotze by thinking the Shema, according to Rav Chisda, Chazal nevertheless obligated a Ba'al Keri to think the Shema in his heart, whilst everyone else is reciting it, in order that he should not be different than everybody else - i.e. *they* are all reciting the Shema, whilst he is sitting idle.

(c) If someone began the Amidah and then remembered that he was a Ba'al Keri, he should cut each Berachah short.

(d) The Gemara initially thought that Chazal did not obligate a Ba'al Keri to think the entire Amidah, because it does contain Malchus Shamayim, like Keri'as Shema.

(e) However, this contention is rejected, because if so, why *did* Chazal obligate him to Bensch, since Benching, like the Amidah, does not contain Malchus Shamayim.
Consequently, the reason that Chazal did *not* obligate him to say the Amidah must be because it is only mi'de'Rabbanan, whereas Keriy'as Shema and Bensching, which are both d'Oraysa, they *did*.