- If oil was placed on the kometz of a מנחת חוטא
Amoraim discuss: קומץ דמנחת חוטא ששמנו – if one placed oil on the kometz of a sinner’s minchah, Rebbe Yochanan says it is פסול, but Reish Lakish says: הוא עצמו משכשכו בשירי הלוג ומעלהו – one should rub [the kometz] itself with the remnants of a log of oil from another minchah and offer it up on the מזבח. Meaning, one should ideally rub this kometz along the inside of a כלי which contains drops of oil from a minchah it previously held; therefore, the kometz certainly remains valid if oil was placed on it. The Gemara objects that the passuk says "לא ישים עליה שמן" – he shall not place oil on it [the מנחת חוטא]! It answers: ההוא שלא יקבע לה שמן כחברותיה – that is teaching that he should not set oil for it like other [menachos], i.e., before the kemitzah, but he can (and should) place some oil on the kometz afterwards.
- Two menachos or their elements became mixed together
The next Mishnah states: שתי מנחות שלא נקמצו ונתערבו זו בזו – two menachos to which kemitzah had not been performed became mixed with each other, אם יכול לקמוץ מזו בפני עצמה ומזו בפני עצמה – if one can do kemitzah from this one separately and do kemitzah from this one separately (i.e., enough of each minchah remained separate, allowing for its kemitzah), both menachos are valid, but if not, they are invalid. If a kometz became mixed with a minchah before its kemitzah, he cannot burn the mixture on the מזבח, since the mitzvah of burning only applies to a kometz, not the rest of the minchah (he also cannot remove two קמצים from the mixture, since each kometz may include flour from the other minchah). However, if he did burn it on the מזבח, the minchah which had been נקמץ counts for its owner, but the minchah which had not been נקמץ does not count for its owner.
- Machlokes about נבילה and שחוטה being מבטל each other (בתר מבטל or בתר בטל)
Rav Chisda says: נבילה בטילה בשחוטה – neveilah [meat] becomes nullified by shechted [meat], meaning if one piece of נבילה became mixed with two pieces of שחוטה, the נבילה is בטל, so a person who touches one piece is not tamei. Although Rebbe Yehudah holds that מין במינו does not become בטל, אי אפשר לשחוטה שתעשה נבילה – it is impossible for שחוטה to become [tamei like] נבילה, so they are not considered מין במינו. However, שחוטה would not become בטל among more pieces of נבילה because it is possible for נבילה to become [tahor like] שחוטה, דלכי מסרחה פרחה טומאתה – because when it spoils, its tumah departs. Therefore, it is considered מין במינו, and not בטל. Rebbe Chanina says the reverse: כל שאפשר לו להיות כמוהו אינו בטל – any mixture where [the minority] can become like [the majority], it is considered מין במינו and not בטל, and where the minority cannot become like the majority, it is not considered מין במינו, and is בטל. The Gemara explains that Rav Chisda holds בתר מבטל אזלינן – we follow the nullifying [item] when determining which item can become like the other, whereas Rebbe Chanina holds בתר בטל אזלינן – we follow the [item] becoming nullified.