R. Yosi holds that Sunday was Rosh Chodesh:

On Sunday Moshe did not address Benei Yisrael, because they were weary from travelling;

On Monday he told them "V'Atem Tihyu Li Mamleches Kohanim";

On Tuesday he told them the Mitzvah of Hagbalah (fencing off Har Sinai);

On Wednesday he told them to abstain from relations.

Chachamim hold that Monday was Rosh Chodesh:

On Monday Moshe did not address Benei Yisrael, because they were weary from travelling;

On Tuesday he told them "V'Atem...";

On Wednesday he told them about Hagbalah;

On Thursday he told them to abstain from relations.

Question (against R. Yosi): "V'Kidashtem ha'Yom u'Machar" (there were only two days of abstention)!

Answer (for R. Yosi): Moshe himself decided to add a third day (so all of Yisrael would be Tehorim).

(Beraisa - R. Yosi): Moshe himself decided to do three things, and Hash-m agreed to all of them - he added a day of abstention, he separated from his wife, and he broke the Luchos. (Tosfos - even though the Gemara brings Moshe's 'source' for each, in every case it is not a real Drashah or Kal va'Chomer, for we say that Moshe himself decided.)

Question: What did he expound to justify adding a day?

Answer: It says "Ha'Yom u'Machar" - today should be like tomorrow, i.e. a full day, including the night;

Hash-m said this during the day, so "Ha'Yom" could not mean today (Wednesday, according to R. Yosi) - rather, it means Thursday (in addition to the rest of today), and 'Machar' refers to Friday).

Question: What is the source that Hash-m agreed?

Answer: The Shechinah did not descend until Shabbos.

Question: What did he expound to justify separating from his wife?

Answer: He made a Kal va'Chomer - Hash-m spoke with Benei Yisrael only once, and he fixed a time, yet He required them to abstain from relations - "V'Hayu Nechonim...Al Tigshu [El Ishah]";

Hash-m speaks with me at all times, without fixing a time - all the more so I should abstain!

Question: What is the source that Hash-m agreed?

Answer: It says "Lech Emor Lahem Shuvu Lachem l'Ohaleichem" (Benei Yisrael should return to their wives) "V'Atah Po Amod Imadi" (but you should remain with Me. Tosfos - surely, Moshe intended to separate before Hash-m said this - otherwise, Miryam and Aharon would not have disapproved).

Some learn from "Peh El Peh Adaber Bo" (this rebutted the disapproval of Moshe's separation).

Question: What did he expound to justify breaking the Luchos?

Answer: Korban Pesach is just one of 613 Mitzvos, it says "V'Chol Ben Nechar Lo Yochal Bo" (one estranged from Hash-m may not eat it) - all the more so, the entire Torah should not be given to Benei Yisrael, for they are Mumarim (on account of the Egel)!

Question: What is the source that Hash-m agreed?

Answer: Reish Lakish expounded "Asher Shibarta" - Yeishar Kochacha (your strength should be increased) for having broken them.

Question (against R. Yosi): "V'Hayu Nechonim la'Yom ha'Shelishi".

Answer: We already said that Moshe added a day!

Question (against Chachamim - Beraisa): It was the third (this will be explained), it was the third of the month, it was Yom ha'Shelishi (Tuesday - this shows that Rosh Chodesh was on Sunday. Tosfos - really, this question [like many to follow] is against Rava, who says that they argue about which day was Rosh Chodesh - R. Yosi and Chachamim only [explicitly] discussed which day of Sivan was Matan Torah.)

Answer: The Beraisa is like R. Yosi.

Question: What is the significance of [the first time it says] 'It was the third'?

Answer: (It was the third day from [Rosh Chodesh,] when he began discussing the reward and punishment of Torah with Yisrael, like Rebbi in the coming Beraisa. Maharsha - this could be discussed even though Yisrael were weary from travelling, only new commands had to be postponed.)

(Beraisa) Question: It says "Va'Yashev Moshe Es Divrei ha'Am El Hash-m" and "Va'Yaged Moshe Es Divrei ha'Am El Hash-m" - what did Hash-m tell Moshe, what did Moshe tell Benei Yisrael, what did Benei Yisrael reply to Moshe, what did Moshe reply to Hash-m?

Answer #1 (R. Yosi b'Rebbi Yehudah): They discussed Mitzvas Hagbalah (even though it is not explicitly mentioned until later, there is nothing else to which to attribute this dialogue).

Version #1 - Answer #2 (Rebbi): First, he told them the punishment [for transgressing Torah] - "Va'YaSHeV Moshe", words that MeSHoVev the mind (cause one to refuse);

Afterwards, he told them its reward - "Va'YaGeD Moshe", things that interest a person, like AGaDa (non-Halachic teachings).

Version #2 - Answer #2 (Rebbi): First, he told them the reward - "Va'Yashev Moshe", words that Meshiv (revive) the mind;

Afterwards, he told them the punishment - "Va'Yaged Moshe", words as bitter as Gidin (wormwood).

Question (against Chachamim - Beraisa): It was the sixth, it was the sixth of the month, it was Yom ha'Shishi (Friday, i.e. Rosh Chodesh was on Sunday).

Answer: Also this Beraisa is like R. Yosi.

Question: What is the significance of [the first time it says] 'It was the sixth'?

Answer #1 (Rava): It was the sixth day from [Sunday,] when they camped [in Midbar Sinai].

Answer #2 (Rav Acha bar Yakov): It was the sixth day from when they left [Refidim].

They argue about the Mitzvah of Shabbos given at Marah:

(Rav Yehudah): "(You must observe Shabbos) Ka'Asher Tzivcha Hash-m Elokecha" - like you were commanded at Marah.

Rava holds that in Marah we were commanded about [most laws of] Shabbos, but not about Techumim (therefore, we could travel on Shabbos - perhaps they left Refidim on or before Shabbos. Tosfos - here 'Techumim' refers to Hotza'ah - Chachamim say that the Isur Techumim is only mid'Rabanan. Even though "Al Yetzei..." is written earlier, and it is expounded to forbid Hotza'ah, Rava must say that it was commanded after Matan Torah and written in in the most appropriate place, i.e. Parshas Man.)

Rav Acha holds that we were also commanded about Techumim (since they camped on Sunday, they must have left that same day).

Question (against Chachamim - Beraisa): In Nisan of Yetzi'as Miztrayim, Benei Yisrael slaughtered Korban Pesach on the 14th, they left on the 15th, at night the Bechoros were stricken...

Interjection: Makas Bechoros was before Benei Yisrael left!

Correction: Rather, they were stricken the previous night.

Continuation of Beraisa: The 15th was on Thursday.

Inference: (Normally, Nisan is full (has 30 days) and Iyar is Chaser (has 29).) This implies that Iyar began (i.e. Rosh Chodesh was) on Shabbos, and Sivan began on Sunday (like R. Yosi)!

Answer: Chachamim say that Iyar was full that year (so Iyar began on Monday. Magen Avraham (494:1) asks why Shavu'os is the 50th day after Pesach - all agree that Pesach was on Thursday, and Matan Torah on Shabbos, the 51st day after Pesach! Maharsha (Avodah Zarah 3A) - day 50 completed the Taharah of Benei Yisrael necessary for Matan Torah. Ravina (86B) was unsure whether or not some people had to immerse on Shabbos - he must have had an answer to this question unlike the Maharsha - PF.)

Question (against Chachamim): Iyar was Chaser that year!

(Beraisa): In Nisan of Yetzi'as Miztrayim, Shechitas Pesach on the 14th, Benei Yisrael left on the 15th, the Bechoros were stricken the previous night; the 15th was on Thursday;

Iyar began on Shabbos; Iyar was Chaser, so Sivan began on Sunday.

Answer: This Beraisa is like R. Yosi.

Question (against Chachamim - Rav Papa - Beraisa): "Va'Yis'u me'Elim... ba'Chamishah Asar Yom la'Chodesh ha'Sheni" - it was Shabbos, for it says "U'Voker u'Re'isem Es Kavod Hash-m " and "Sheshes Yomim Tilketuhu" (i.e. manna will fall for six days, starting tomorrow morning).

Since Iyar 15 was Shabbos, Sivan began on Sunday.

Answer: Chachamim say that Iyar was full.

Question (Rav Chavivi of Chuzna'ah - Beraisa): "Va'Yhi ba'Chodesh ha'Rishon ba'Shanah ha'Shenis be'Echad la'Chodesh Hukam ha'Mishkan" - there were 10 special things about that day:

It was the first day of creation [Sunday], the first day the Nesi'im offered Korbanos [for Chanukas ha'Mishkan], the first day of Kehunah, the first day of Avodah, the first day fire descended from Shamayim, the first day Kodshim were eaten, the first day of Shechinah [Bach - among Yisrael], the first day of Birkas Kohanim, the first day that Bamos were forbidden, and [Nisan is] the first month [for Yisrael].

Inference: If Rosh Chodesh Nisan [in the second year] was Sunday, the previous year it was Wednesday;

(Beraisa - Acherim): Shavu'os is always four days later in the week than the previous Shavu'os (the months always alternate full-Chaser, a year is 354 days, 50 weeks and four days); Rosh Hashanah is always four days later than the previous Rosh Hashanah;

In a leap year [we add a month of 29 days, i.e. four weeks and one day], they are separated by five days.

This implies that Iyar [of Yetzi'as Miztrayim] began on Friday, and Sivan began on Shabbos - this is unlike both Tana'im!

Answer: [Acherim say that always, six months between Nisan and Nisan are Chaserim - our Tana'im argue,] R. Yosi says that seven months were Chaserim, so three days separated Nisan and Nisan (not four), so Nisan [of Yetzi'as Miztrayim] began on Thursday, Sivan began on Sunday (even though Acherim agree that sometimes we must have an extra (i.e. seventh) full month in a year (Erchin 9B), because a lunar month is slightly more than 29 and a half days, they would never agree to an extra Chaser month);

Chachamim say that eight months were Chaserim, so the previous Nisan began on Friday, Sivan began on Monday. (Tosfos - they could agree that seven were Chaserim and that Nisan began on Thursday, just Iyar was full, so Sivan began on Monday.)