(R. Elazar): Just like Mitzvos do not nullify each other, Isurim do not nullify each other.

We learn from Hillel that Mitzvos do not nullify each other;

(Beraisa): Hillel used to eat Korban Pesach and Matzah and bitter herbs wrapped together - "Al Matzos u'Morerim Yochluhu" (all are Mitzvos. No one is Mevatel another.)

Pesachim 115a (Rav Mesharshiya brei d'Rav Noson): Hillel had a tradition that after the Churban one should not eat Matzah and Maror wrapped together. Since Matzah is a Mitzvah mid'Oraisa and Maror is only mid'Rabanan, Maror is Mevatel Matzah.

Even the opinion that Mitzvos do not Mevatel each other says this only when both are mid'Oraisa or both are mid'Rabanan. However, if one is mid'Oraisa and the other is mid'Rabanan, the mid'Rabanan is Mevatel the mid'Oraisa.

Question: Who says that Mitzvos are not Mevatel each other?

Answer: Hillel says so. He used to wrap them (Pesach, Matzah and Maror) together and eat them to fulfill "Al Matzos u'Morerim Yochluhu."

(R. Yochanan): Hillel's colleagues disagree:

(Beraisa) Suggestion: Perhaps one wraps them together and eats them like Hillel did!

Rejection: "Al Matzos u'Morerim Yochluhu." (It could have said 'Yochlu'. Rather, it says Yochluhu, and we read this 'Yochal Hu',) one may even eat each by itself.

Objection (Rav Ashi): If so, why does it say even? (This connotes that one may eat them together if he wants!)

Answer (Rav Ashi): Rather, the Beraisa means as follows:

Suggestion: Perhaps one must wrap them together like Hillel did to be Yotzei!

Rejection: "Al Matzos u'Morerim Yochluhu" - one may even eat each by itself.

Conclusion: The Halachah was not fixed like Hillel, nor like Chachamim. (Nowadays) we bless Al Achilas Matzah, eat Matzah, bless Al Achilas Maror, eat Maror, and then eat Korech (both wrapped together) without a Berachah, to commemorate when there is a Mikdash, according to Hillel.

Rif and Rosh (Pesachim 25a and 10:27): Hillel taught that nowadays, if one eats Matzah and Maror wrapped together, Maror is Mevatel Matzah. All agree that a Mitzvah mid'Rabanan is Mevatel a Mitzvah mid'Oraisa.

Question (Ba'al ha'Ma'or): The Rif says that the Beraisa proves R. Yochanan's assertion that Chachamim argue with Hillel. The conclusion was like Rav Ashi, that the Beraisa is like Hillel! It teaches that one need not eat them wrapped together, but one may do so! Rather, R. Yochanan must have had a tradition that Chachamim argue with Hillel.

Answer (Milchamos Hash-m): In the Ba'al ha'Ma'or's text, Rav Ashi explicitly establishes the Beraisa like Hillel. However, the correct text does not. It cannot be like Hillel, for it says 'perhaps one must do like Hillel used to do'. According to Hillel, the Torah requires doing this way! Rav Ashi does not argue with R. Yochanan. Rather, he refutes the Gemara's assertion that there is an opinion that Mitzvos (mid'Oraisa) are Mevatel each other. The Beraisa is like Chachamim, and they agree that one is Yotzei by eating them together! They argue only about whether or not the verse requires eating them together.

Question: Perhaps Hillel holds that normally Mitzvos are Mevatel each other; here is different, because the Torah commanded to eat them together! Chachamim hold that Mitzvos are Mevatel each other, yet they agree that if one ate them together he was Yotzei!

Answer (Mordechai Pesachim 611): If Hillel held that normally Mitzvos are Mevatel each other, he would need the verse to permit eating them together, so he would have no source to require this l'Chatchilah.

Rosh (ibid.): We dip Korech in Charoses, for this is the only time that Hillel would dip in Charoses.

Question: The Gemara implies that had the Halachah been fixed like either opinion, we would act differently. This is not so! Hillel agrees that nowadays we cannot eat them together, for Maror would Mevatel Matzah!

Answer (Rosh ibid.): If the Halachah were like Hillel, we would bless on Matzah and eat it, then bless on Maror and eat it with Matzah. Since Maror and Korech are both mid'Rabanan, they do not Mevatel each other.

Question: If (according to the Rif) Chachamim agree that equal Mitzvos do not Mevatel each other, we should be able to do so according to everyone! Why must we eat Maror by itself?

Answer (Rosh ibid. and Milchamos Hash-m): Perhaps the Halachah follows Chachamim; they hold that Korech is Reshus (not a Mitzvah at all), it would be Mevatel Maror (a Mitzvah mid'Rabanan), just like a mid'Rabanan is Mevatel a mid'Oraisa.

Rambam (Hilchos Chametz u'Matzah 8:6): One takes two Matzos, breaks one, puts the piece inside the whole Matzah and blesses ha'Motzi. Afterwards he wraps Matzah and Maror together and blesses 'Al Achilas Matzos u'Morerim' and eats them. If he ate each of them by itself he blesses on each of them by itself.

Magid Mishnah: This is when there is a Mikdash, and Matzah and Maror are both mid'Oraisa, so neither is Mevatel the other.

Rambam (ibid. 8:8): Nowadays one blesses ha'Motzi and Al Achilas Matzah, dips the Matzah in Charoses and eats it. Then he blesses Al Achilas Maror, dips the Maror in Charoses but does not leave it in very long, and eats it. This is a Mitzvah mid'Rabanan.

R. Mano'ach (DH v'Lo): Even though it is a Mitzvah mid'Rabanan to dip in Charoses, since the Torah mentions Maror but not Charoses, Maror is like mid'Oraisa compared to Charoses. Therefore, the Charoses would Mevatel the Maror if the Maror was left in for a while. We are not concerned lest Charoses Mevatel the Matzah because one need not taste the Matzah. Alternatively, Matzah is dry and it does not absorb much taste.

Question: If Matzah is made from rice and grain, we do not say that rice of Reshus is Mevatel grain of Mitzvah (Zevachim 78a)!

Answer #1 (R. David Pesachim 115a DH v'Ifshar): We are concerned lest there will be enough Maror to Mevatel the taste of Matzah. Alternatively, perhaps the Maror will be a Chatzitzah between the Matzah and his throat.

Answer #2 (R. David ibid. and Tosfos 78a DH Ela): Maror is Mevatel Matzah, for its taste is potent. Alternatively, Maror is Mevatel some taste of the k'Zayis of Matzah. If the Korech contains a larger Shi'ur of Matzah, one is Yotzei.

Question (Gilyon ha'Shas Zevachim ibid.): Nowadays, after eating Matzah by itself we eat Maror by itself. We do not eat it with Matzah, for then Matzah is Reshus and it would Mevatel Maror, even though Matzah's taste is not potent!

Answer #1 (Keren Orah 78a DH v'Ein): Chachamim hold that Mitzvos are Mevatel each other. Regarding Min b'Mino, the minority is Batel, one was not Yotzei that Mitzvah. Regarding Min b'Eino Mino, if each can be tasted neither is Batel. However, l'Chatchilah they should be eaten separately.

Answer #2 (Magihah in R. David, 19): Since there is a Mitzvah to taste the Maror, we are concerned even for a slight blunting of its taste.

Answer #3 (Maharam Chalavah 115a DH v'Asi, citing the Ramban): Here, we do not discuss Bitul of taste. Rather, it was enacted to do each Mitzvah by itself.

Note: To answer the previous question, the Ramban can say that Matzah made of rice and grain is one entity (they were mixed before it received the name Matzah, at the time of baking), so it is considered doing the Mitzvah by itself.

Griz (Zevachim ibid.): We are concerned for Bitul of the Mitzvah, not of the taste! Nevertheless, if one can taste the Matzah he is Yotzei because Ta'am k'Ikar.

Question (Griz): In Zevachim, Rashi says that Hillel teaches that we are not concerned lest Maror be Mevatel the taste of Matzah. Why doesn't he address Bitul of the Pesach? Rashi holds that Pesach is eaten together with Matzah and Maror!

Note: Rashba (Berachos 38b DH Lo) proves from the law of Bitul that we require the taste of Matzah. Perhaps Rashi holds that we learn from a Hekesh to Maror (reason dictates that taste of Maror is required), but we do not require the taste of Pesach. Alternatively, he teaches that Maror is not Mevatel Matzah, and all the more so it is not Mevatel Pesach, for meat has a more potent taste than Matzah.

Shulchan Aruch (OC 475:1): One holds together the three Matzos with the broken one in the middle, blesses ha'Motzi and Al Achilas Matzah...and eats a k'Zayis from each. Afterwards he fully submerges a k'Zayis of Maror in Charoses but does not leave it in very long, lest it lose its bitterness. For this reason one must shake the Charoses off. He blesses Al Achilas Maror and eats it without reclining. Afterwards he cuts the bottom Matzah and wraps a piece together with Maror and dips them in Charoses.