Question: What is the source for the prohibition of Melachah on Chol ha'Moed?

Answer #1 (R. Oshiya): "You shall observe Chag ha'Matzos for seven days" (Shemos 23:15) implies that on Chol ha'Moed it is also Asur to do Melachah.

Answer #2 (R. Yonasan): It is a Kal v'Chomer that on Chol ha'Moed it is Asur to do Melachah.

The days surrounding Chol ha'Moed (the first and seventh days of the festival) are Asur b'Melachah, and

The days of Chol ha'Moed have a Musaf offering, and

The days of Chol ha'Moed are called "Mikra Kodesh" (Vayikra 23:4), so certainly they should be Asur b'Melachah!

Answer #3 (R. Yosi ha'Glili): "You may not do any work of Melachah" (Vayikra 23:7-8) teaches that Chol ha'Moed is Asur b'Melachah.

Answer #4 (R. Akiva): "These are the festivals of Hash-m..." (Vayikra 23:4) teaches that Chol ha'Moed is Asur b'Melachah.

Answer #5 (Beraisa): "For six [more] days you shall eat Matzah, and on the seventh day shall be a cessation to Hash-m, you may not do any work" (Devarim 16:8).

The six days [of Chol ha'Moed] are compared to the seventh day; just like the seventh day is Asur b'Melachah, so, too, the six days.

The six days [of Chol ha'Moed] are not Asur in all forms of Melachah, though, because the verse specifically mentions "on the seventh day."

Rather, the Torah gave the authority to the Chachamim to teach which Melachah is Asur and which Melachah is Mutar.

Question: It happened once that R. Tarfon did not permit a eulogy to take place on the Yom Tavo'ach (the day of bringing the Korbanos of Shavuos (presumably when Shavuos fell on Shabbos and its Korbanos were brought on Sunday)!

This contradicts our Mishnah, which says that eulogies are permitted on Sunday, when Shavuos falls on Shabbos and its Korbanos are brought on Sunday!

Answer: In that incident, Shavuos fell during the week, and its Yom Tavo'ach was not on Sunday.

The first type of "Ma'alah": different levels of purifying oneself to eat, or touch, different items:

Chulin, Ma'aser, and Terumah require Netilas Yadayim (washing the hands).

Kodesh requires Tevilas Yadayim (immersing the hands in a Mikvah).

Mei Chatas requires Tevilah of the entire body.

The second type of "Ma'alah:"

If one immersed himself in a Mikvah with intention to purify himself for eating one level (e.g. Chulin), he is Asur to eat the higher level (e.g. Ma'aser).

But if one immersed himself for a higher level, he may eat an item from a lower level.

If he immersed without any intention at all, it is as if he did not immerse.

The third type of "Ma'alah:" The clothing of an Am ha'Aretz is a "Midras" (i.e. Tamei) for one who eats Chulin b'Taharah, and likewise for the higher levels of Taharah.

Question: Do Chulin and Ma'aser really need Netilas Yadayim?

But the Beraisa says that only Terumah needs Netilas Yadayim!

Answer: Our Mishnah is the Rabanan, who say (Parah 11:5) that Chulin needs Netilas Yadayim, while the Beraisa is Rebbi Meir, who says that Chulin and Ma'aser do not need Netilas Yadayim.

Question: That answers only Chulin, but we do not find anyone who says that Ma'aser needs Netilas Yadayim!

Answer: Our Mishnah is referring to eating bread of Ma'aser, which requires Netilas Yadayim, while the Beraisa is referring to eating fruit of Ma'aser, which does not need Netilas Yadayim.

As Rav Nachman said, anyone who washes his hands to eat fruit is considered haughty.

Question: One Beraisa says that one must have intention when washing or immersing one's hands, while another Beraisa says that even without intention, one becomes Tahor!