(Mishnah): If a Chulin onion fell into Terumah lentils - if the onion was whole, the lentils are permitted (to non-Kohanim). If it was cut up, they are prohibited if the onion can be tasted (when eating the lentils). If it had fallen into other foods, whether the onion was whole or cut up, they are prohibited if the onion can be tasted. R. Yehuda permits pickled fish (if an uncut onion of Terumah had been left inside it and then removed) since the onion was only to absorb the bad fish flavor. (Note: Although many (such as the Rosh, Rash, Rav O. Mi'Bartenura) understand that Mishnah's case is in fact when a Terumah onion fell into Chulin lentils, it is clear from the upcoming Gemara that the Yerushalmi understood the Mishnah as described, that a Chulin onion fell into Terumah lentils.)

If a Terumah apple was chopped and put into a Chulin dough and it leavened, it is prohibited (to non-Kohanim). If Terumah barley fell into a pit of water, even though the barley causes the water to spoil, the water is permitted.

(Gemara): The Mishnah taught that if a Chulin onion fell into Terumah lentils etc.

(R. Chizkiyah/R. Achai citing R. Ba bar Mamal): The Mishnah's permitted case is when he removed the lentils from their water, as the lentils shrink the onion that it should not absorb. And just as you say that the lentils shrink it so that it doesn't absorb; similarly, the lentils shrink it so it doesn't give off its flavor.

The Mishnah is discussing when a Chulin onion fell into Terumah lentils, but not if a Terumah onion fell into Chulin lentils, (as in such a case, even if the onion was whole, it gives its flavor into the lentils).

The permission when it was a whole onion only applies to when it was dry, not moist; to an onion, not a turnip; as for a turnip, whether dry or moist, whole or cut, it is prohibited. If he removed its upper part (Pitam), it's as if it was cut. If two or three small onions fell in, they are considered cut.

A whole onion is permitted only when the outer shell is so dry that it does not give flavor (to the lentils), but if it does, it is prohibited.

(Mishnah in Maseches Maaser Sheni): If fish was cooked with Maaser Sheni turnips and the dish improved, the value of the improvement is calculated according to the relative quantities. (For example, if the fish was worth two Dinars and the turnips were worth one Dinar and the dish improved and became worth 4 Dinars, the extra Dinar is divided between them accordingly, so when he wishes to redeem the Maaser Sheni turnips, 1 1/3rd Dinars are redeemed.)

(R. Hoshiya): The Mishnah in Maaser Sheni does not follow R. Yehuda in our Mishnah, who permits pickled fish (if an uncut onion of Terumah had been left inside it and then removed) since the onion was only to absorb the bad fish flavor.

Question (Rabbanan of Kisarin): When R. Abahu said from R. Yochanan that for all prohibitions (that became mixed with something permitted and it cannot be clarified as to whether it was enough to give flavor), we evaluate it as if it's an onion or turnip (whose flavors pervade much more since they are sharp). This is unlike R. Yehuda who said that onion and turnip do give flavor to fish...?

Answer: R. Yehuda agrees if the onion is of Hekdesh or idolatry (since its prohibited to gain any benefit from these items).

The Mishnah taught that if a Terumah apple was chopped and put into a Chulin dough and it leavened, it is prohibited (to non-Kohanim).

Baraisa (R. Yosi): It is permitted (since fermenting in this way is not considered fermenting),

(R. Acha/ R. Abahu citing R. Yosi b'R. Chanina): Rabbanan and R. Yosi disagree over when the apple was chopped and its juices were put into the dough, but if a whole apple was put into the dough, all agree that it's not considered a full fermenting and the dough is permitted to non-Kohanim.

Just as R. Yosi said there (in a Mishnah in Maseches Shabbos, that R. Yosi permits breaking an egg into a cloth that was heated by the sun, since the heat is a derivative of the sun with which one may cook) that its cooking is not considered cooking; so too here its fermenting is not considered fermenting.

Tosefta (R. Meir): When a prohibition gives flavor, whether it improves or worsens the taste, it is prohibited.

(R. Shimon): If it improves it, it is prohibited; if it worsens it, it is prohibited.

(R. Shimon ben Lakish): The dispute is when it first improved and then worsened; but if it first worsened and then improved, even R. Meir agrees that it is permitted.

(R. Yochanan): The dispute is in both cases.

(Mishnah in Maseches Orlah): If barley (of Terumah) fell into a pit of water, even if the water spoiled, it is permitted (since it worsened the taste of the water (both beginning and end).

How does this fit with R. Yochanan and R. Shimon ben Lakish?

R. Yochanan says that R. Meir would disagree (and prohibit the water). R. Shimon ben Lakish says that all agree that the water is permitted.

(R. Yosi bar R. Bun): R. Yochanan and R. Shimon ben Lakish explicitly disagree and take this positions.