(Mishnah): One who ate Demai [we are Mezamen with him].

Inference: If one ate [his own] Peros, and it is a Safek whether or not they were tithed, we are Mezamen [with him].

Rebuttal (R. Shimon, the brother of R. BeraChiya): When they decreed about Demai, most Amei ha'Aretz used to enter [the Peros] into their houses [and tithe them]. Does this say [that we are Mezamen when it is an even Safek]?!

Defense: We are Mezamen with a Kusi. Is not a Kusi a Safek [Nochri]?

Note: This shows that we are Mezamen amidst Safek, but not that we learn this from Demai.

Rebuttal (R. Aba): [Our Mishnah] is like the opinion that a Kusi is like a Yisrael. [Tana'im] argued about this;

(Beraisa): A Kusi is like a Nochri. Rebbi says so. R. Shimon ben Gamliel says, a Kusi is like a Yisrael in every way.

(Mishnah): We do not include women, slaves or children in a Zimun;

Question: How much [must one eat] to be Mezamen with him?

Answer #1: [He must eat at least] a k'Zayis;

Answer #2 (R. Yehudah): [He must eat] at least a k'Beitzah.

(Gemara - R. Simon citing R. Yehoshua ben Levi, and R. Yosi ben Sha'ul citing Rebbi): They made a minor an adjunct to [join to] 10.

Question (Beraisa): We are not meticulous about a minor (e.g. if he reached 13 years, we are Mezamen with him even if we are unsure if he brought hairs. This implies that if we know that he did not bring two hairs, we are not Mezamen with him, i.e. even to join to 10!)

(R. Yosi): R. Simon answered this in the name of R. Yehoshua ben Levi - [the Beraisa] discusses two minors, one is a Safek [adult] and one is a [Vadai] minor. We consider the Safek like a Vadai [adult], and the [Vadai] minor is an adjunct [to 10. However, we do not join two Vadai minors to 10.]

(R. Yudah bar Pazi citing R. Yosi): If nine look like 10, they are Mezamen [like 10. We explained this like CHAREDIM.]

Question: Does this refer to esteemed people?! (Surely, even nine esteemed people do not have the law of 10! - MAHARA FULDA)

Answer: Rather, there is a minor [among the 10].

Question (R. BeraChiya citing Yakov bar Zavdi): I asked R. Yosi, just like you say that a minor, we make him an adjunct to 10, you should say that here, we make him an adjunct to three!

There, that we mention Hash-m's name (say Elokeinu in the Zimun, when there are 10), we make him an adjunct - here (a Zimun of three), that we do not mention Hash-m's name, all the more so!

Answer (R. Yosi): This is not all the more so (rather, just the contrary)! There, [there is a Zimun without the minor]; in order to say Hash-m's name, we make him an adjunct. Here, we do not say Hash-m's name (rather, we want to join him to make a Zimun), we do not make him an adjunct. (We explained this like R. SHLOMO SIRILIYO.)

(Beraisa): A minor and a Sefer Torah [in his hand] - we make him an adjunct.

(R. Yudan): [No,] the Beraisa means that a minor [called] to [read from also Sefer Torah, we make him an adjunct (he counts towards the seven Aliyos on Shabbos. We explained this like CHAREDIM.)

Question: From what age do we make him an adjunct?

Answer (R. Avina): Rav Huna and Rav Yehudah argued about this, both in the name of Shmuel. One said that it is from when he knows the meaning of the Brachah. The other said that it is [even] from when he knows to Whom he blesses.

(R. Nasa): Several times I ate with my father R. Tachlifa and with my uncle Aniniya bar Sisi, and they were not Mezamen on me (to rely on e to be the third) until I brought two hairs.