במדבר פרק ט, ו
וַיְּהִי אֲנָשִׁים אֲשֶׁר הָיוּ טְמֵאִים לְנֶפֶש אָדָם וְלֹא-יָכְלוּ לַעֲשת- יֵנְפִל וּבְרְק
יַו אוּהַה םוֹיַב חַסֶפַה
משֶׁה וְלִפְנֵי אַהֲרֹן בַיוֹם הַהוּא :
מסכת סוכה דף כה/ב
אותם אנשים מי היו עוסקין במת מצוה היו שחל שביעי שלהן להיות בערב פסח שנאמר ולא יכלו לעשות הפסח ביום ההוא ביום ההוא אין יכולין לעשות הא למחר יכולין לעשות
Rashi explains that the Gemara is not necessarily discussing a dead person that has no apparent relatives (Mais Mitzvah), but the concept of Mais Mitzvah can also include a dead person that a Cohen becomes tameh in order to bury. Why does Rashi use so much language to explain that the case involves permission to bury the dead person? What difference is it if the case only involved a dead person that did not have any relatives?
However, one must explain that the Gemara is teaching that one that is engaged in a “light” mitzvah is exempt from “harder” mitzvos. The event that a person discovers a dead body within 7 days of Pesach, and burying the body would result in being tameh for Pesach and prevent one from eating the Korban Pesach. Nevertheless, a person does not pass by the “easy” mitzvah (burying the body) due to losing the future, more “stringent” mitzvos involving Pesach.
If the Gemara was trying to learn this concept only from a Mais Mitzvah, then that would be problematic since everyone (even a Cohen Gadol) needs to become involved. Thus, Rashi understood that the concept includes even becoming tameh for one’s relatives, and then the concept could be conveyed.
In addition, why did the Gemara ask the question in the first place regarding who was tameh? What difference did it make? However, Rashi explains (Parshas Ki Sisa) that between the two countings (the first of Tishrei and the first of Iyar) nobody died. Thus, the Gemara asks who was tameh connected to a dead person, if no one had died. And the Gemara then answers with several answers.
Touching a Sefer Torah Results in Tumah to the Hands
במדבר פרק י, לה וַיְּהִי בִּנְסֹעַ הָאָרֹן
מסכת ידים פרק ג משנה ה מְגִּלָה שֶׁכָתוּב בָּהּ שְמוֹנִים וְחָמֵש אוֹתִיוֹת, כְפָרָשַת "וַיְּהִי בִּנְסֹעַ הָאָרֹן" - מְטַמָא אֶת הַיָדַיִם. כָּל כִּתְבֵי הַקֹדֶש - מְטַמְאִין אֶת הַיָדַיִם.
The decree of tumah to the hands by directly touching a Sefer Torah, results from the early times where one would being eating Terumah and would store the leftover in the Sefer Torah, because they thought this is holy and the Terumah is holy, so let them be together. However, the result was that the mice would eat the food plus damage the Sefer Torah. Thus, the initial decree was that any Terumah that touched a Sefer would become tameh like a third degree of tumah. Not only this, but the decree was expanded that anyone that touched a Sefer their hands would be a second degree of tumah. The decree included not only a Sefer Torah, but any of the holy writings (Nach).
