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Yevamos Chart #18

Yevamos Daf 61b-62a

FULFILLING THE MITZVAH OF PIRYAH V'RIVYAH
  (A)
BEIS SHAMAI 		(B)
BEIS HILLEL
1) OUR MISHNAH 2 sons(2)(4) 1 son and
1 daughter(1)(3)
2) REBBI NASAN
(1ST VERSION) 		2 sons and
2 daughters(5) 		1 son and
1 daughter(3)
3) REBBI NASAN
(2ND VERSION) 		1 son and
1 daughter(3) 		1 son *or*
1 daughter(6)
==========
FOOTNOTES:
==========
(1) The Yerushalmi says that Beis Hillel means that one fulfills the Mitzvah of Piryah v'Rivyah by having either one male and one female, *or* by having two males (for males are preferable to females for the purpose of fulfilling this Mitzvah, as implied by the Gemara at the beginning of 62b). Accordingly, Beis Hillel is lenient as compared to Beis Shamai (which is consistent with the fact that this Machlokes is not recorded among the Kulos of Beis Shamai in Eduyos, ch. 4). This is also the view of TOSFOS CHAD MI'KAMAI and PISKEI RID, as well as the RASHBA in TESHUVOS (3:339). However, the RASHBA in his comments to our Gemara, as well as the other Rishonim here, reject this explanation and prove that the Bavli argues with the Yerushalmi on this point. According to the Bavli, Beis Hillel holds that one only fulfills Piryah v'Rivyah with one male and one female, and not with two males.
(2) RASHI explains that Beis Shamai holds that one fulfills the Mitzvah with specifically two males, and *not* with one male and one female. (This is also clear from the Yerushalmi mentioned in footnote #1). However, a different text of Rashi is cited by the RASHBA, ME'IRI, and RABEINU AVRAHAM MIN HA'HAR, in which Rashi says that Beis Shamai holds that both having two males, or one male and one female, is a fulfillment of the Mitzvah, and Beis Shamai is being more lenient than Beis Hillel. (They ask, however, that according to this explanation this Machlokes should have been included among the Kulos of Beis Shamai in Eduyos -- see Rashba.)
(3) This is learned from the creation of the world. See Insights to 61b.
(4) This is learned from Moshe Rabeinu, who separated from his wife after having two sons.
(5) This is learned from the children that Adam and Chavah bore.
(6) This is because having even one child "settles the world."

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