Sukkah, Chapter 1, Mishnah 11. The Mishnah opens with the law of a sukkah that has no actual roof, and then moves on to discuss whether a mat is valid for use as sechach.
"Ha'oseh sukkaso k'min tzerif o sh'semachah la'kosel":
"Ha'oseh sukkaso k'min tzerif" - one who builds his sukkah like a hut, which has no flat roof at all, but rather two slanted walls that meet each other at an angle above, forming a sort of triangle.
"O sh'semachah la'kosel" - that he leaned one wall against another wall. Here too there is no roof, only walls.
Rabbi Eliezer invalidates in both cases, since in his opinion a sukkah must have a roof of at least a tefach.
"Va'chachamim machshirin" - in their opinion the slanted wall itself is considered a roof.
A mat that is susceptible to tumah and a mat that is not susceptible to tumah:
The Mishnah now turns to a mat made from material that is fit for sechach, except that the manner in which it was made determines its law: if it was made in a way that it is susceptible to tumah, it is invalid for sechach; and if it is not susceptible to tumah, it is valid. As a general rule:
A large mat: its ordinary use is for covering and for sechach, and it is not susceptible to tumah.
A small mat: its ordinary use is for lying on and it is considered a mattress, and therefore it is susceptible to tumah and invalid for sechach.
The words of the Tanna Kamma:
"Im asa'ah lishchivah - mekabbeles tumah v'ein mesachchin bah" - we are dealing with a large mat, for even though its ordinary use is not for lying on, here he designated it specifically for lying on, contrary to its usual use, and therefore it is susceptible to tumah and one may not use it for sechach.
"Asa'ah l'sichuch - mesachchin bah v'einah mekabbeles tumah" - we are dealing with a small mat, for even though its ordinary use is for lying on and it is susceptible to tumah, here he made it specifically for the purpose of sechach, and therefore it is valid and not susceptible to tumah.
The Mishnah must be read this way: the first clause, which says that he made it for lying on, does not fit a small mat, since its ordinary use is already for lying on and there is no need to designate it for that; perforce it speaks of a large mat that he designated contrary to its usual use. And so too the reverse: the second clause, which says that he made it for sechach, does not fit a large mat, since its ordinary use is already for sechach and there is no need to designate it for that; and from the fact that the Mishnah specified that he made it for sechach, it is proven that it deals with a small mat, for that is not its usual use.
The opinion of Rabbi Eliezer:
"Achas ketanah v'achas gedolah" - in Rabbi Eliezer's opinion there is no difference between a small mat and a large mat, since according to his approach "he made it for lying on" means that he made it without any particular intent, without a conscious decision, and in any case it stands by default to be used for lying on. Therefore both are susceptible to tumah and one may not use them for sechach. However, if he made it specifically for sechach, contrary to its default status and contrary to its usual use, one may use it for sechach and it is not susceptible to tumah.
In summary: in this Mishnah we learned two matters. The first - a sukkah built like a hut, or one leaned against a wall, which has no roof but only slanted walls: Rabbi Eliezer invalidates it because a roof of a tefach is required, while the Sages validate it and view the wall itself as a roof. The second - the law of the mat: a mat designated for lying on is susceptible to tumah and invalid for sechach, and one designated for sechach is not susceptible to tumah and is valid. According to the Tanna Kamma everything depends on designating it contrary to its usual use, and therefore the first clause speaks of a large mat and the second clause of a small mat; whereas according to Rabbi Eliezer there is no distinction between small and large, since a mat by default stands to be used for lying on, unless he made it explicitly for the purpose of sechach.