and those who are impure do not perform the ritual of the Paschal lamb on the first Pesaḥ or the second. They do not perform the ritual of the Paschal lamb on the first Pesaḥ because they are not the majority, and the Paschal lamb may be sacrificed in a state of impurity only when the majority of the community is impure. Additionally, they may not perform the ritual of the Paschal lamb on the second Pesaḥ because they are not the minority, and only the sacrifice of a minority of the community is deferred to the second Pesaḥ.

The Gemara raises an objection from that which we learned in the mishna: If the entire community became ritually impure, or if most of it became impure, or if the priests were impure and the community was pure, they should perform the ritual of the Paschal lamb in impurity. This indicates that it is only when most of the community is impure that they perform the ritual of the Paschal lamb in impurity, but if it is half and half, they do not perform the ritual of the Paschal lamb on the first Pesaḥ. This poses a difficulty to the opinion of Rav.

Rav could have said to you: When a majority of the community is impure, they may all perform the ritual of the Paschal lamb in impurity. Even those who are still pure are not required to ensure that they remain pure in order to sacrifice the Paschal lamb. When it is half and half, these who are pure perform the ritual of the Paschal lamb for themselves in a state of purity and these who are impure perform the ritual of the Paschal lamb for themselves in a state of impurity.

The Gemara adds: So too, it is reasonable to understand the mishna in this way, as the latter clause teaches: If a minority of the community became impure, those who are pure perform the ritual of the Paschal lamb on the first Pesaḥ and those who are impure perform the ritual of the Paschal lamb on the second Pesaḥ. This indicates that it is only when the minority has become impure that they perform the ritual of the Paschal lamb on the second Pesaḥ. But when it is half and half this is not the case; rather, these perform the ritual of the Paschal lamb for themselves in a state of purity and those perform the ritual of the Paschal lamb for themselves in a state of impurity on the first Pesaḥ.

However, if so, it then poses a difficulty to the opinion of Rav Kahana. The Gemara responds: Rav Kahana could have said to you that the latter clause of the mishna should be understood as follows: If a minority of the community became ritually impure, those who are pure perform the ritual of the Paschal lamb on the first Pesaḥ and those who are impure perform the ritual of the Paschal lamb on the second Pesaḥ. This indicates that if it is half and half, those who are pure perform the ritual of the Paschal lamb on the first Pesaḥ and those who are impure do not perform the ritual of the Paschal lamb on the first or the second Pesaḥ.

The Gemara asks: This works out well according to the latter version of Rav Kahana’s statement, according to which this is the halakha when exactly half of the community is pure and half is impure. But according to that first version, in which Rav Kahana said that when half the community is pure and half is impure, those who are pure perform the ritual of the Paschal lamb on the first Pesaḥ and those who are impure perform the ritual of the Paschal lamb on the second Pesaḥ, what is there to say?

Rav Kahana could have said to you that the mishna should be understood as follows: The same is true even in a case of half and half as well; those who are pure perform the ritual of the Paschal lamb on the first Pesaḥ, and those who are impure perform the ritual of the Paschal lamb on the second Pesaḥ. And that which was taught in the mishna that the sacrifice of a minority of the community is deferred to the second Pesaḥ is not meant to indicate that half the community cannot observe the second Pesaḥ. Rather, since it taught in the first clause of the mishna the case in which the majority of the community became ritually impure, it also taught in the latter clause the case in which the minority of the community became impure, so as to employ a parallel formulation.

The Gemara points out that it was taught in a baraita in accordance with the opinion of Rav, and it was taught in a baraita in accordance with the opinion of Rav Kahana, in accordance with each of the two versions of his opinion. It was taught in the following baraita in accordance with the opinion of Rav: If the Jewish people were divided, and half were pure and half were impure, those who are pure perform the ritual of the Paschal lamb for themselves in a state of purity, and those who are impure perform the ritual of the Paschal lamb for themselves in a state of impurity on the first Pesaḥ.

It was taught in the following baraita in accordance with the first version of the opinion of Rav Kahana: If the Jewish people were divided, and half were pure and half were impure, those who are pure perform the ritual of the Paschal lamb on the first Pesaḥ, and those who are impure perform the ritual of the Paschal lamb on the second Pesaḥ.

And it was taught in the following baraita in accordance with the latter version of the opinion of Rav Kahana: If the Jewish people were divided, and half were pure and half were impure, those who are pure perform the ritual of the Paschal lamb on the first Pesaḥ, and those who are impure do not perform the ritual of the Paschal lamb on the first Pesaḥ or the second Pesaḥ.

The Gemara asks: According to Rav and according to the latter version of the opinion of Rav Kahana, with regard to that which was taught in the second baraita quoted above, that those who are pure perform the ritual of the Paschal lamb on the first Pesaḥ and those who are impure perform the ritual of the Paschal lamb on the second Pesaḥ, how do they reconcile it? The Gemara answers: According to them, the case under discussion is one where the Jewish people are divided, and half are pure and half are impure. However, the majority of the men are pure, and the majority of the women are impure and the women complete the number of impure people necessary to reach half of the community.

And this tanna holds that the participation of women in the first Pesaḥ is optional. Therefore, remove the women from those who are impure, and the impure become the minority. And the sacrifice of the minority is deferred to the second Pesaḥ according to all opinions.

The Gemara asks: According to the opinion of Rav and according to the first version of the opinion of Rav Kahana, with regard to that which was taught in the third baraita cited above: Those who are pure perform the ritual of the Paschal lamb on the first Pesaḥ and those who are impure do not perform the ritual of the Paschal lamb on the first Pesaḥ or on the second Pesaḥ, how do they reconcile it according to their opinions?

Rav reconciles the baraita by explaining that it is referring to a case where the men of the Jewish people were divided, and half were impure and half were pure, and the women, a majority of whom were pure, added on to the number of those who were pure so that the majority of the community was pure. And this tanna holds that the participation of women in the first Pesaḥ is obligatory, and their participation in the second Pesaḥ is optional.

Therefore, on the first Pesaḥ, those who are impure do not perform the ritual of the Paschal lamb because they are a minority, and a minority of the community that is ritually impure may not perform the ritual of the Paschal lamb on the first Pesaḥ. And on the second Pesaḥ they do not perform the ritual of the Paschal lamb because when one removes the women from them, those who were impure are half of the community, and half the community does not perform the ritual of the Paschal lamb on the second Pesaḥ.

And according to the first version of the opinion of Rav Kahana, in which he said that half the community also performs the ritual of the Paschal lamb on the second Pesaḥ, this is how he would reconcile the baraita with his opinion: It is addressing a case where the Jewish people were divided, and half were pure and half were impure. However, the majority of the men were impure, and it is the women who completed the necessary number of the pure so that the division was half and half. And this tanna holds that the participation of women on the first Pesaḥ is obligatory, and their participation on the second Pesaḥ is optional.

Therefore, on the first Pesaḥ they may not perform the ritual of the Paschal lamb because they are half and half, and according to his opinion, half of the community may not perform the ritual of the Paschal lamb on the first Pesaḥ in a state of impurity. On the second Pesaḥ as well, they may not perform the ritual of the Paschal lamb because one must remove the women from the number of those who are pure, and the impure become the majority, and the majority does not perform the ritual of the Paschal lamb on the second Pesaḥ.

The Gemara asks further: And according to Rav Kahana, with regard to that which was taught in the first of the three baraitot above: If the Jewish people were divided, half were pure and half were impure, those who were pure perform the ritual of the Paschal lamb for themselves on the first Pesaḥ, and those who were impure perform the ritual of the Paschal lamb for themselves on the second Pesaḥ, how does he reconcile it? Rav Kahana could have said to you: This matter is subject to a dispute between the tanna’im. There is one who said that in a case of half and half, each half by itself is considered like the majority, and there is one who said that half and half is not like the majority.

The Gemara addresses the matter itself discussed in the baraita cited previously. If the Jewish people were divided, half were pure and half were impure, those who were pure perform the ritual of the Paschal lamb for themselves on the first Pesaḥ and those who were impure perform the ritual of the Paschal lamb for themselves on the second Pesaḥ. If those who were impure outnumbered those who were pure even by one person, they should perform the ritual of the Paschal lamb in ritual impurity on the first Pesaḥ because a communal offering is not divided. Therefore, the entire community may sacrifice the Paschal lamb in a state of impurity. This includes those who were pure; they do not need to take care to remain pure in order to sacrifice the Paschal lamb.

Rabbi Elazar ben Matya says: The individual cannot tip the balance of the entire public toward ritual impurity, as it is stated: