Gemara

Mishnah: Children are exempt from Sukah. If a child does not need his mother, he is obligated.

Question: Our Mishnah exempts children, and a Beraisa expounds "Kol" to include children!

Answer: A child is obligated only if he reached the age of Chinuch (training in Mitzvos).

Question: Chinuch is only mid'Rabanan (but the Beraisa expounded a verse)!

Answer: The verse is a mere Asmachta.

Eruvin 82a - Rav Asi: A woman's Eruv (also) permits her six year old son.

Question (Beraisa): A woman's Eruv permits her son only if he needs her (and we shall show that this is before six)!

Mishnah: A boy that does not need his mother is obligated in Sukah.

Question: When do we say that he does not need his mother?

Answer #1 (D'vei R. Yanai): This is when he eliminates and his mother does not wipe him.

Answer #2 (R. Shimon (ben Lakish)): This is when he does not call for his mother when he wakes up.

Objection: Even mature children call for their mothers when they wake up!

Correction: Rather, when he wakes up he does not call for her repeatedly until she comes.

This is a child of four or five.

Answer (Rav Yehoshua brei d'Rav Idi): Rav Asi discusses a child whose father and mother were Me'arev for him in different directions. A boy of six prefers the company of his mother, therefore her Eruv permits him.

Question (Beraisa): A woman's Eruv permits her son only if he needs her. This is until six years. (Rav Yehoshua requires the parent to Mezakeh for the child. The Beraisa gives the same law for all children below six, and surely no Zikuy is needed for an infant!)

Rav Yehoshua is refuted.

Suggestion: This also refutes Rav Asi (who permits even a six year old. The Beraisa permits until (but not including) six!

Rejection: No, it means, Ad v'Ad Bichlal (up to and including six).

Suggestion: Also R. Yanai and Reish Lakish are refuted (they say that a child of four or five does not need his mother. But such a child is not permitted with his mother's Eruv, and this Beraisa permits even a six year old!)

Rejection: A child of four or five does not need his mother if his father is around. The Beraisa permits a six year old whose father is not around, for he needs his mother.

Rishonim

The Rif and Rosh (2:17) bring the Mishnah and the opinions of d'Vei R. Yanai and Reish Lakish about when a child does not need his mother.

Ran (DH Masnisin): When we say that a child of five or six years is obligated mid'Rabanan, this means that we must put him in a Sukah.

Ran (DH Gemara): We learn from Eruvin that a child of six does not need his mother.

R. Yehonason (on Rif Eruvin 27a DH Gemara): A child of six does not need his mother when his father is away. The Gemara says that if the father is here, a child of four does not need his mother.

Bach (8): The Rif, Rambam and most Meforshim explain that Rav Asi does not distinguish whether or not the father is here, unlike d'Vei R. Yanai and Reish Lakish.

Rambam (Hilchos Sukah 6:1): Children are exempt from Sukah. If a child does not need his mother, which is a child of about five or six years, he is obligated mid'Rabanan for Chinuch.

Source (Magid Mishnah): Eruvin 82a suggests that the age is five or six.

Question (Beis Yosef OC 440 DH u'Masnisin and DH umi'Kol): D'Vei R. Yanai and Reish Lakish themselves said that the Shi'ur for Sukah is four or five. Why does the Rambam adopt the Shi'ur given regarding Eruvin instead?

Answer (Beis Yosef, ibid.): The Yerushalmi says that the Shi'ur for Sukah and Eruv are the same. The Shi'ur of four or five regarding Sukah was not brought in its place (Sukah 28b), so it is not reliable.

Question: If so, the Rambam should simply say a boy of six, like the Shi'ur for Eruv!

Answer (Beis Yosef, ibid.): The Rambam explains that the Gemara says 'six years' when the father is here, and this refers to the beginning of year six. The Rambam calls this five (i.e. after five complete) years. The Rambam says 'or six', i.e. after six full years and beginning the seventh, regarding a child whose father is away.

Question (Lechem Mishneh): The Gemara in Eruvin connotes that the Shi'urim are the same. Had the Rambam explained in one place (Sukah or Eruv) that the Shi'ur is four or five when his father is here and six if he is away, we could say that the same applies to the other place. But the Rambam did not explain in either place!

R. Mano'ach: The Shi'ur is when he mother does not wipe him after he eliminates. This is five or six.

Rosh (Eruvin 8:2): A child up to six is Yotzei with his mother's Eruv if his father is away. When the father is here, he is Yotzei only if he is at most four or five.

Poskim

Shulchan Aruch (OC 640:2): If a child does not need his mother, which is a child of about five or six years, he is obligated in Sukah mid'Rabanan for Chinuch.

Taz (2): The Rif and Rambam do not distinguish whether or not the father is here, because this answer is only for d'Vei R. Yanai and Reish Lakish. Rav Asi answered that the Beraisa means Ad v'Ad Bichlal. The Halachah follows Rav Asi, for only his opinion is brought in Kesuvos (65b).

Question: Regarding Eruv, the Rosh and Tur (Sof 414) distinguish whether or not the father is here. Regarding Sukah they do not distinguish (even though the distinction was said to defend the opinion of d'Vei R. Yanai and Reish Lakish regarding Sukah!

Answer #1 (for the Tur - Beis Yosef DH umi'Kol): The Tur says 'six or seven', i.e. six when the father is here, and seven when he is away.

Objection (Taz 2): It this was the Tur's intent, surely he would have explained so!

Answer #2 (Taz 2): The Rosh and Tur hold that all the Amora'im equate Sukah and Eruv. Rav Asi says that the Shi'ur is six, without distinction (whether or not the father is here). D'Vei R. Yanai and Reish Lakish distinguish. The Rosh and Tur are stringent like d'Vei R. Yanai and Reish Lakish regarding Eruv, so when the father is here they forbid to (rely on the mother's Eruv and) take a six year old outside the Techum. Chinuch is mid'Rabanan, so regarding Sukah the Rosh and Tur are lenient like Rav Asi, to be passive and exempt a younger boy even if his father is here. This is why they mention that Chinuch is mid'Rabanan, i.e. therefore he is exempt until he finished six years and began the seventh.

Levushei Serad (13): The Shulchan Aruch refers to five or six full years, depending on the maturity if the child. Even though the Beis Yosef questioned the Rambam, he rules like him.

Gra (DH k'Ven): The text of the Shulchan Aruch should say 'five (complete) years which is six years.' Had the Shulchan Aruch ruled like d'Vei R. Yanai and Reish Lakish, it would have said four or five years and distinguished between the presence and absence of the father.

Mishnah Berurah (4): Several Acharonim hold that if a boy is five years or more, if his father is here he does not need his mother so much so he is obligated, even if he is not so mature.

Beis Yosef (DH Kasuv bi'Srumas): The Terumas ha'Deshen says that it seems that there is no Chiyuv of Chinuch for a boy without a father. However, one should not be lenient.

Mishnah Berurah (5) and Sha'ar ha'Tziyon (8): If he has no father, some say that his mother and Beis Din must train him. In any case no may put food in his mouth or tell him to eat outside the Sukah. However, except for his father, one may put food in front of him and let him eat by himself.