Eiruvin 91 - 97
The Tenth Man
If the wall separating two courtyards of different sizes collapses so that the smaller one is completely open to the larger one, and the larger one retains "wings" on either side of the opening, an interesting relationship is created between the two courtyards. The smaller courtyard is viewed as an extension of the larger one, and the opening between them is viewed as a mere doorway leading to the larger area. The larger courtyard, however, cannot be viewed as an extension of its smaller neighbor which it has absorbed.
This relationship of the smaller area being dominated by the larger one has ramifications not only in the laws of eruv (if the residents of the houses in the larger courtyard made an eruv, they may carry from their houses to the courtyard; i.e., they are unaffected by the fact that they did not make an eruv together with the residents of the smaller one, while the residents of the smaller courtyard may not carry from their houses to their own courtyard, because of the domination of their neighbors in the larger courtyard) but also in regard to a wide range of halachic matters. One of the most interesting ramifications relates to forming a minyan for prayer from ten Jews located in two such adjoining courtyards.
If there are nine Jews in the larger courtyard and one in the smaller courtyard, the one in the smaller courtyard is considered as being in their area together with them, and we therefore have a valid minyan. But if nine are in the small courtyard and one is in the larger courtyard, that individual is not considered as being in the area of the nine, and we do not have a minyan.
The simple reading of this gemara would indicate that the only criterion is that the majority of the minyan not be in the smaller area; However, Tosefos points out that there is also a need for the majority of the minyan to be in the larger area. If there are five men in the larger one and five in the smaller one, concludes Tosefos - and thus rules the Shulchan Aruch (Orach Chaim 55:16) - there is no minyan. A majority must be located in the larger area so that the minority in the smaller area is considered as being "pulled" into that area and group to form the minyan.
A Blessing for the Exempt
A woman is not obligated to perform mitzvos which are time-oriented, such as the mitzvah of tefillin which cannot be performed at night or on Shabbos or Holidays. There is no ban, however, on their doing so. It is common practice for women to come to the synagogue to hear the shofar on Rosh Hashana and to shake the four species on Succos, even though women are exempt from these time-oriented mitzvos.
As proof that there is nothing improper in a woman performing a mitzvah from which she is exempt, the gemara cites the example of King Saul's daughter Michal who used to put on tefillin, and the wife of the Prophet Yonah who was accustomed to making a pilgrimage to Jerusalem during the three Festivals. In neither case was any objection raised by the Sages.
But can a woman who performs such a mitzvah say the blessing which a man says before performing it - "Blessed are You ... who commanded us concerning the mitzvah of ..." - even though she was not actually commanded to do so?
Tosefos cites the opinion of Rabbeinu Tam that she may say this blessing. One proof is that Michal probably did so, and if no objection was raised we may conclude that there is no problem in a woman praising Hashem for commanding Israel as a nation to perform the mitzvah.
Another proof cited by Rabbeinu Tam raises an interesting problem: According to the Sage Rabbi Yehuda, a blind man is not obligated in mitzvos by the Torah. There is evidence from another source (Kiddushin 31a) that although he is exempt, he can say a blessing on any mitzvah that he performs. This invites a comparison to a woman, and serves as additional support for the position that a woman can also say a blessing on mitzvos from which she is exempt.
Tosefos, however, challenges this proof by suggesting that a blind man is obligated in mitzvos by Rabbinic Law, and can therefore say a blessing praising Hashem for commanding us to obey the laws which the Sages decreed, while women are not obligated in time-oriented mitzvos even by Rabbinic Law.
Why did the Sages not obligate women in mitzvos, as they did the blind? Tosefos offers two explanations, one of which is as follows: Women have mitzvos which are not bound by time to distinguish them as Jews, while the blind, if not for the Sages obligating them, would be virtually indistinguishable from non-Jews because of their total exemption.
The halacha, however, is that the blind are obligated in all mitzvos by Torah Law, as is the position of the Sages who dispute Rabbi Yehuda's view. Regarding women saying a blessing on mitzvos from which they are exempt, the Beis Yosef rules like the opinion of Rambam that they should not do so. Rema, on the other hand, rules like Rabbeinu Tam that women should say a blessing (Shulchan Aruch Orach Chaim 589:6). This accounts for the varying customs of different communities. It is the universal custom, however, to discourage women from performing the mitzvah of tefillin altogether (ibid. 38:3).