OPINIONS: In the Mishnah (72a), Beis Shamai and Beis Hillel argue whether five groups of people in one large hall separated from each other by Mechitzos are considered one large group or five separate groups. The Gemara records four opinions concerning the exact point of dispute between Beis Shamai and Beis Hillel (see Chart):

1. They argue only when the Mechitzos are nothing more than low dividers made of strips of wood ("Mesifas"), but when the Mechitzos are ten Tefachim high they agree that the Mechitzos effectively divide the five groups.

2. They argue both when the groups are separated by nothing more than a "Mesifas" and when they are separated by Mechitzos that are ten Tefachim high.

3. They argue when the Mechitzos reach the ceiling, but when the Mechitzos do not reach the ceiling they agree that the Mechitzos do not separate the groups.

4. They argue when the Mechitzos do not reach the ceiling, but when the Mechitzos do reach the ceiling they agree that the Mechitzos separate the groups from each other.

The Gemara (72b) cites a Beraisa in which Beis Shamai and Beis Hillel argue only when the Eruv is brought from the five groups in the hall to another place (in order to make an Eruv between all of the other houses in the Chatzer). In contrast, when others bring the Eruv to the hall, all of the groups in the hall are considered to be one group.

How does this Beraisa understand the argument between Beis Shamai and Beis Hillel in the Mishnah, and what point does it add to the Mishnah? Is it elaborating on the opinion of Beis Hillel, or is it discussing only the opinion of Beis Shamai?

(a) TOSFOS (DH Aval) and the ROSH explain that according to the Beraisa, the argument between Beis Shamai and Beis Hillel applies when the Mechitzos do not reach the ceiling (#4 above). When the Mechitzos do reach the ceiling, Beis Shamai and Beis Hillel agree that the groups are considered separate. The Beraisa is discussing a case in which the Mechitzos reach the ceiling, but, nevertheless, if the Eruv is brought to the hall, then the groups in the hall are considered joined. Accordingly, the Beraisa is teaching a leniency according to both Beis Shamai and Beis Hillel.

(b) The RITVA explains that according to the Beraisa, the argument between Beis Shamai and Beis Hillel applies when there is only a ten-Tefach-high Mechitzah between each group (#2 above). The Beraisa is teaching that Beis Shamai agrees that when the Eruv is brought to them, they are considered joined even though there are Mechitzos between them. Accordingly, the Beraisa is teaching a leniency according to Beis Shamai. (This might be the intention of Rashi as well.)

(c) The RASHBA writes that it is not logical to suggest that when the Mechitzos are ten Tefachim high, Beis Shamai maintains that the groups are considered joined if the Eruv is brought to them. Rather, the Beraisa refers to when there is a "Mesifas" between each group, and the Beraisa understands the argument between Beis Shamai and Beis Hillel the same way that the second version of Rav Nachman does (#2 above). The Beraisa means that according to Beis Shamai, each group must contribute separately to the Eruv only when they bring the Eruv to another location. When the Eruv is brought to them, Beis Shamai agrees that they are all considered one group.