1) MIXTURES OF CHAMETZ ON PESACH
OPINIONS: Rava concludes that the Halachah follows the opinion of Rav, who rules that even a minute amount of Chametz forbids a mixture when it falls into a non-Chametz food on Pesach. A "Mashehu" (any amount) of Chametz is forbidden "Bein b'Mino, Bein she'Lo b'Mino," whether it became mixed with the same type of food or with a different type of food.
Why is the law with regard to a mixture of Chametz more stringent than the law with regard to all other prohibitions? In every other case of a prohibited food item, when a prohibited food becomes mixed with a similar type of food (but one that is permitted), it prohibits the mixture only when it comprises a majority (Rov) of the mixture. When a prohibited liquid becomes mixed with a permitted liquid, it prohibits the mixture only "b'Nosen Ta'am," when enough of the forbidden item is present such that its taste is noticeable in the mixture (this amount is defined practically as 1/60th; see REMA, Yoreh De'ah 98:1).
(a) RASHI (29b, DH she'Lo b'Mino) writes that Rav maintains that in the case of all prohibited foods, a mixture of "Min she'Lo b'Mino" is prohibited "b'Nosen Ta'am," and a mixture of "Min b'Mino" is prohibited "b'Mashehu." The only difference between Chametz and other prohibitions is that Chametz is also prohibited "b'Mashehu" when the mixture is "Min she'Lo b'Mino." In the case of other prohibited foods that fell into a mixture of "Min she'Lo b'Mino," the mixture is prohibited only "b'Nosen Ta'am."
Rashi explains that this difference is due to the severity of the prohibition of Chametz. Chametz is more severe than other prohibitions because it is punishable with Kares. Moreover, people are not accustomed to refraining from Chametz (11a), as they eat it throughout the year. Rav therefore maintains that even a mixture of "Min she'Lo b'Mino" is prohibited "b'Mashehu," like a mixture of "Min b'Mino."
(b) TOSFOS (DH Amar Rava) argues with Rashi, who says that a mixture "Min b'Mino" of any other prohibition is also prohibited "b'Mashehu." Tosfos asserts that a mixture of "Min b'Mino" is not prohibited "b'Mashehu," but only "b'Rov," when the prohibited item comprises a majority of the mixture. This is the opinion of the Rabanan. The reason Chametz is prohibited "b'Mashehu," even in a mixture of "Min b'Mino," is because of the severity of Chametz, as Rashi explains. Because of the severity of the prohibition, the Rabanan decreed that both "Min b'Mino" and "Min she'Lo b'Mino" are prohibited "b'Mashehu."
(c) The RAMBAM (Hilchos Ma'achalos Asuros 16:9) and the RAN explain that the reason Chametz is prohibited "b'Mashehu" is because Chametz is a "Davar she'Yesh Lo Matirin," it is a forbidden item which eventually will become permitted. Since one can wait until after Pesach to eat the mixture, the mixture is prohibited "b'Mashehu" on Pesach. Rava rules like Rebbi Shimon who maintains that after Pesach, Chametz that was owned by a Jew is prohibited only mid'Rabanan. The Rabanan did not prohibit Chametz after Pesach when the Chametz is mixed with another food. Therefore, since one can wait to eat the mixture until after Pesach, when the mixture will be permitted, on Pesach it is prohibited "b'Mashehu."
The RAN casts doubt on this reasoning. Even though a mixture of Chametz is permitted after Pesach, Chametz that is distinct and not mixed is indeed prohibited (mid'Rabanan) after Pesach. Therefore, Chametz cannot be called a "Davar she'Yesh Lo Matirin."
The MORDECHAI (#553) suggests another reason for why Chametz is not considered a "Davar she'Yesh Lo Matirin." The Chametz does not become indefinitely permitted after Pesach, because it will become forbidden at a later time -- next Pesach. Therefore, it cannot be called a "Davar she'Yesh Lo Matirin."
(d) RABEINU TAM (cited by Tosfos DH Amar Rava) and the BA'AL HA'ME'OR have a different text in the Gemara. According to their text, Rava does not say that a mixture of Chametz is "forbidden b'Mashehu," but merely that it is "forbidden." Rava means to say that it is forbidden "b'Nosen Ta'am," in accordance with the opinion of Rebbi Yochanan. Accordingly, there is no difference between Chametz and all other prohibitions. This is also the opinion of the SHE'ILTOS.
HALACHAH: The SHULCHAN ARUCH (OC 447:1) rules like Tosfos, that mixtures of all other Isurim of "Min b'Mino" are prohibited only "b'Shishim" (when the Isur is more than 1/60th of the Heter), and a mixture with Chametz (both "Min b'Mino" and "Min she'Lo b'Mino") is prohibited "b'Mashehu," due to the severity of the Isur.
However, the MISHNAH BERURAH (447:2) adds that when there are pressing reasons to be lenient, one may rely on the view of the She'iltos and use a mixture with Chametz as long as it is not "Nosen Ta'am."
With regard to whether Chametz is considered a "Davar she'Yesh Lo Matirin," both opinions are cited by the REMA (YD 102:4) and the SHACH (YD 102:14).
There is a practical difference between the two reasons for why a mixture of Chametz is forbidden even "b'Mashehu" -- the severity of the prohibition of Chametz, or the fact that Chametz is a "Davar she'Yesh Lo Matirin." If the reason is because of the severity of the prohibition of Chametz, then the mixture with a "Mashehu" is forbidden only when the punishment of Kares applies. On Erev Pesach after the sixth hour and before nightfall, Chametz is forbidden but there is no punishment of Kares. As a result, a mixture of "Min b'Mino" will not be forbidden "b'Mashehu" on Erev Pesach before nightfall, according to Tosfos. However, according to the Rambam, a mixture of Chametz on Erev Pesach will be forbidden "b'Mashehu," because it is a "Davar she'Yesh Lo Matirin," which will become permitted after Pesach. (MAGID MISHNEH, Hilchos Chametz u'Matzah 1:5)
The SHULCHAN ARUCH (OC 447:2) rules that a mixture of Chametz on Erev Pesach is permitted if the quantity of Chametz is only a "Mashehu." It is evident from this ruling that the Shulchan Aruch does not agree with the Rambam, and he maintains that Chametz is not a "Davar she'Yesh Lo Matirin."