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Are women to recite Kiddush Levana?
 Slaves: Slaves are exempt from reciting Kiddush Levana just as is the law by women. [Siddur Yaavetz]
 Admur 106:2 “Women are exempt from all time dependent positive commands even if they are Rabbinical, such as Hallel and Kiddush Levana”; M”A 426:1 in name of Shlah Shaar Haosiyos Kuf and M”A 296:11; M”B 426:1
The reason: As it is a time dependent Rabbinical positive command. [Admur ibid; M”A ibid and 70:1] This is because the month may only be sanctified in its first half.
Other opinions: Some Poskim rule that Kiddush Levana is not a time dependent command. [Chochmas Shlomo on M”A ibid who questions this concept] See Haelef Lecha Shlomo 193; Maharil Diskin Kuntres Acharon 26; Yalkut Hagershoni 426; Likkut Dinei Rosh Chodesh 12 footnote 12
 Peri Megadim 426 A”A 1 based on the reason brought in Shelah and M”A ibid; M”A 296:11 “Women are not accustomed to recite Kiddush Levana”
The reason: Although women are allowed to perform Mitzvos which they are exempt from, nevertheless they should not say Kiddush Levana, being that it was a woman who was responsible for the diminishing of the moon, as it was caused due to the sin of Eve. [Shlah ibid; M”A ibid; See Minchas Yitzchak 8:15 and 34-1] Alternatively, the reason is because women may only recite a blessing on a time dependent positive command if the command contains an action, however when the entire command is fulfilled in speech, then women may not recite it. [M”A 296:11 in opinion of Rama 296:8; Chasam Sofer 34; Maharam Shick 56] Practically however, the Poskim negate this reason. [Bach brought in M”A ibid; Admur 296:11]
Other opinions: The Gemara in Sanhedrin 42a states that the short blessing of Kiddush Levana is “said by our women.” This implies that women would say Kiddush Levana. Some Poskim rule that women are to hear the blessing from others and recite it. [Kaf Hachaim 426:1 based on Sanhedrin 42a] Other Poskim however, negate this ruling of the Gemara, explaining that the wording refers to igonoramouses and not actual women. [M”A 426:1 that it is Practically this is not the custom. The Peri Megadim 426 A”A 1 writes it is implied that women are not to say Kiddush Levana even without a blessing.