Question: Granted, the (other) Isurim of our Mishnah (an animal had bestiality.,..) are not recognizable. What is the case of Treifah?

If it is recognizably Treifah, we can remove it and offer the others. If it is not recognizably Treifah, how do we know that a Treifah is among them?

Sukah 9b (Mishnah): If one draped a vine over a Sukah, it is Pasul. If there was more Sechach than vines or if he cut them, it is Kosher.

9b - Question: If he did not do Chavatah, why it is Kosher? Pasul Sechach joins with Kosher Sechach! (Chavatah means separating the attached Sechach from the Kosher Sechach, cutting what was attached, lowering the vine and mixing it with the Kosher Sechach, or knocking the leaves off the vines.)

Answer: We must say that he did Chavatah.

Bechoros 25b (Beraisa): A Ba'al Mum forbids any quantity (that it is mixed with);

R. Yosi says, one checks.

This cannot mean to check which is the Ba'al Mum and to remove it. The first Tana would not disagree!

Makos 16b (Rabah bar Rav Huna): If one ground up nine ants and completed a k'Zayis with an ant that is Chai, he is lashed for eating a k'Zayis of Neveilah.

(Rav Yosef): The same applies if one minced ant and a Chai ant comprised a k'Zayis.

They do not argue. Rabah discusses small ants, and Rav Yosef discusses very big ants.

Rif (Sukah 6a): The Gemara established our Mishnah to be when he did Chavatah. If not, Pasul Sechach joins with Kosher Sechach, and it is Pasul.

Rambam (Hilchos Sukah 5:13): If one combined Kosher and Pasul Sechach, even if the majority is Kosher it is Pasul.

Rambam (16): If one put Kosher and Pasul Sechach next to each other, if there is more Kosher Sechach it is Kosher. If there is exactly the same of both it is Pasul, because Pasul Sechach is like Parutz.

Magid Mishnah: It is as if the Pasul Sechach is not there, therefore we need a majority of Kosher Sechach.

Rosh (Chulin 8:20): One piece of Isur is Batel in two pieces of Heter when they are mixed and the Isur is not Nikar. Bitul does not apply when the Isur is Nikar.

Rosh (Sukah 1:14): Rashi says that 'Chavtan' means that he lowered the vine and mixed it with the Kosher Sechach. The vine is Batel in a majority of Kosher Sechach.

Mordechai (Sukah 734): R. Shimshon explains that Sechach under the tree is Pasul. Therefore, even though there is mostly shade, the Gemara asked that Pasul Sechach (what is under the tree) joins with Kosher Sechach. When Chavtan, the branches do not disqualify the Sukah, for they are the minority (and are mixed with the Sechach), like one who put Kosher Sechach in between metal poles.

Mordechai (735): Why are we concerned for an upper Sukah if the lower Sukah has more shade than sun? This is good according to R. Shimshon. Pasul Sechach disqualifies Sechach below it. If the top Sukah is Kosher, the Sechach below it becomes Pasul and Batel.

R. Ovadya mi'Bartenura (Shekalim 1:1 DH v'Al): Beis Din announces about Kil'ayim, that people diminish other species (mixed with seeds) to less than one part in 24. Raboseinu explain that after it grows, even if 1 part in 1000 was mixed in, everything must be uprooted. Bitul does not apply when two permitted species are mixed and the mixture is Asur. At the time of seeding it suffices to diminish, for mid'Oraisa one part in two is Batel, and this is not called seeding Kil'ayim. One must diminish due to Mar'is Ayin (lest it look like he transgresses). After they grew, Bitul does not apply. One must uproot everything and leave only one species.

Tosfos Yom Tov (Kil'ayim 2:1): He explains that mid'Oraisa one part in two is Batel; Chachamim forbid due to Mar'is Ayin. They said that less than one part in 24 is Batel. This is astounding. Bitul b'Rov applies only when they are not Nikarim! Different species of grain are Nikar, and all the more so grain and pulse (a legume). I say that Chachamim knew that the Torah forbids only when he wants to plant Kil'ayim. Chachamim forbade this due to Mar'is Ayin, and gave a Shi'ur.

Chachmas Shlomo (OC 632:1): The Bartenura proves, like the Levush, that Bitul applies even to something Nikar. The case of minced ants is a proof for the Levush.

Note - he understands, like Rashi (16b DH Mishum), that 'Chai' is a live ant. It is Batel in the minced ants, even though it is Nikar. Tosfos (DH Risek) says 'Chai' means intact, for a live ant would not join to the Shi'ur. Even Rashi said that it joins only because it dies when he eats it. Rav Yosef obligates for one minced ant and a Chai ant that comprise a k'Zayis. Chachmas Shlomo must say that this is only when the minced ant is bigger, so the live ant is Batel in it.

Shulchan Aruch (YD 109:1): If a dry piece was mixed with other pieces Min b'Mino, one in two is Batel.

Rema: This is when one does not recognize the Isur. It it was mixed Min b'Eino Mino and one does not recognize the Isur, one needs 60 for Bitul.

Rema (OC 626:1): One should not make a Sukah under a tree.

Shulchan Aruch: If one did, and the Sukah gives mostly shade only with the tree, one must lower the branches and mix them with the Sechach so they are not Nikarim. We need a majority of Sechach, and then the branches are Batel to the Sechach.

Question: Normally, l'Chatchilah we may not Mevatel an Isur!

Answer (Magen Avraham 3, according to Machatzis ha'Shekel DH mi'Kol): Since there is enough Sechach by itself, we do not need the branches, so there is no intent to be Mevatel an Isur. However, it is not clear how to answer for the opinion that allows the branches to join with the Sechach to create a majority of shade.

Bi'ur Halachah (DH v'Ye'arvem): It cannot be Nikar which is the Kosher and Pasul Sechach. If one put the Pasul Sechach on the Kosher, this is Nikar, and they do not join to Machshir if the Kosher Sechach has more sun than shade.

Shulchan Aruch (ibid.): Some say that even if the tree allows more sun and the Sukah itself gives mostly shade without the tree, if the branches are over directly over the Sechach it is Pasul, whether the tree or Sukah was there first.

Magen Avraham (2): It is Kosher even if he did not lower the branches. Tosfos and the Rosh proved this, since when the Kosher and Pasul Sechach are equal, it is Kosher, even though Chavtan does not cause Bitul b'Rov, for they are Nikarim. They are not mixed; each is by itself.

Rema: However, if one lowered the branches and mixed them with the Sechach so they are not Nikarim, they are Batel and it is Kosher.

Bach (DH v'Al): Rashi, Tosfos and most Meforshim explain like this. When it is not Nikar, mid'Oraisa the Pasul is Batel in the majority. If the Pasul Sechach is Nikar, it is not Batel.

Rebuttal (Magen Avraham 4): This is only when the Sukah itself gives mostly shade. The tree does not join. It is totally Batel; it does not join or disqualify. This is like the Ran and Rosh. The Rema's words 'so they are not Nikarim' are imprecise. The law is even if it is Nikar, since the Sukah is mostly shade. The Rema merely uses words parallel to the previous law.

Rema: Similarly, if one put Kosher Sechach on the Pasul Sechach this is a mixture, and it is Kosher.

Darchei Moshe ha'Aruch (3:2, brought in Hagahah 14 in Shulchan Aruch ha'Shalem): The Mordechai says that if one put Sechach on the shingles, this is better than a regular mixture. This is a totally different Sechach.

Hagahos (Shulchan Aruch ha'Shalem, 14): This is not in our texts of the Mordechai.

Bi'ur Halachah (DH Mikri): Chemed Moshe and Ma'amar Mordechai say that according to the Rema, if the Kosher Sechach is on bottom, they must be mixed so that they are not Nikarim. If the Kosher Sechach is on top, they need not be mixed. It suffices to lower it. They say that there is no difference. The Mordechai and R. Shimshon hold that Chavtan does not mean mixed, rather, lowered. It suffices that they touch each other.

Shulchan Aruch (632:1): If there is less than three Tefachim of Pasul Sechach in a minimal Sukah of seven by seven Tefachim, it is Kosher and one may sleep under it. It joins to complete the Shi'ur for a Sukah.

Levush (1): The Pasul Sechach is Batel to the Kosher Sechach, like any Isur that is Batel in Heter. This is difficult, for a Nikar Isur is not Batel! Perhaps it is a tradition from Moshe from Sinai. Alternatively, mid'Oraisa even a Nikar Isur is Batel in the majority, for we learn from the Sanhedrin; a minority (of dissenting judges) is Batel in the majority, even though it is known! Regarding Isurim, one must discard the Isur (when it is Nikar), i.e. mid'Rabanan. Regarding Sukas Mitzvah, Chachamim left the Torah law in effect. Perhaps it is a tradition from Moshe from Sinai.

Rebuttal (Taz): Heaven forbid to say that the Torah does not require discarding a Nikar Isur! Tosfos (Chulin 95a DH Sefeiko) says that mid'Oraisa, one is Batel in two (others) when the Isur is not Nikar. There is no proof from Sanhedrin. There is no mixture there. The Torah said that the minority opinion is Batel. We cannot say that it is reversed to the majority, like we say about mixture of Isur in Heter. Likewise, regarding Sukah, the Pasul less than three Tefachim is Batel, for there is no reason to be Pasul. It is not due to a mixture. Rather, since it is a little, it is as if it is not.

Mishbetzos Zahav (3): The Levush is difficult. If a Nikar Isur is Batel, if we hold that the Torah permits to be Mevatel Isurim, anything can be permitted! One can mix a Neveilah with two slaughtered animals to permit it! There is no proof from Sanhedrin. Since it is not known which is the correct opinion, it is as if the Isur is not Nikar. Only regarding Isurim, it is transformed to Heter. Mid'Rabanan one must cast one away. According to one answer in Tosfos, the Torah requires casting one away.

Chasam Sofer: Here the Bitul is below in the shade, and there it is not Nikar. Regarding Kil'ayim it is not Nikar where the roots nurture, and there there is Bitul. We could remove the Pasul Sechach above and avoid Bitul, and similarly regarding Kil'ayim. We learn from Sanhedrin. The dissenters could remove themselves, and then there would not be a final verdict. We need a verdict with all the judges who began. Perhaps even so they are obligated, and forbidden to remove themselves; their opinion is Batel. The same applies here.

Chasam Sofer (Chulin 11a DH Kegon): Regarding Sanhedrin, the minority is Nikar. It cannot be Batel. One does not take from the minority, just we are not concerned for it. It is as if it is not.

Chasam Sofer (YD 277): Yad Eliyahu said that one Sefer Torah with a mistake is Batel in two others, for the mistake is not an important matter (that is not Batel). Even if there were only three Sifrei Torah in all, he permits using all at once. The Magen Avraham (437:4) says that whenever there is Bitul b'Rov, even if one could check it, we rely on the majority. This is why we do not check for the 18 Treifos. However, whenever an Isur was mixed and it is possible to clarify and recognize it, it is not Batel. The Levush is totally wrong. We could not say that one checks which is the Ba'al Mum to remove it, for surely, all would agree. We did not say that he discusses films in the eye and the animal was mixed with 1000 animals, i.e. and it is hard to check. Rather, if it is possible to check in any way (even if it is very hard) Bitul does not apply. The same applies to a mistake lost in a Sefer Torah.