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Bechor behemah tehorah - why is it given to the cohen?

In this week's sedrah , the Torah says that it is a mitzva to give the bechor of a kosher domesticated animal to the cohen ; כָּל פֶּטֶר רֶחֶם לְכָל בָּשָׂר אֲשֶׁר יַקְרִיבוּ לַה' בָּאָדָם וּבַבְּהֵמָה יִהְיֶה לָּךְ... אַךְ בְּכוֹר שׁוֹר אוֹ בְכוֹר כֶּשֶׂב אוֹ בְכוֹר עֵז לֹא תִפְדֶּה קֹדֶשׁ הֵם אֶת דָּמָם תִּזְרֹק עַל הַמִּזְבֵּחַ וְאֶת חֶלְבָּם תַּקְטִיר אִשֶּׁה לְרֵיחַ נִיחֹחַ לַה'. וּבְשָׂרָם יִהְיֶה לָּךְ כַּחֲזֵה הַתְּנוּפָה וּכְשׁוֹק הַיָּמִין לְךָ יִהְיֶה. " The firstborn of all living things which they (the benei yisroel) bring to Hashem whether from man or from animals shall belong to you (the cohanim ) … But the firstborn of an ox or the firstborn of a sheep or the firstborn of a goat you shall not redeem for they are holy. You shall sprinkle their blood on the mizbeach and you should burn their fat as a fire offering for a pleasing scent to Hashem. And their flesh will be to you like the chest [which is presented as a

Seperating challah from dough which is tameh

The gemara says in Pesachim (32a) that if you seperate terumah from chametz on Pesach then it does not become terumah ; ...מפריש תרומת חמץ דברי הכל אינה קדושה “Everyone agrees that if you separate terumah from chametz on Pesach it does not become terumah .” The gemara in daf 33 explains that this is becuase the passuk says that you have to give terumah to a cohen for him to eat, here the cohen can only use the chametz for making a fire (that is, even according to the ma'an de'amar that chametz on Pesach is mutar behana'ah the maximum benefit the cohen could have is to use the chametz as fire-wood); ...מנא הני מילי? אמר רב נחמן בר יצחק אמר קרא (דברים יח, ד) תתן לו ולא לאורו “How do we know this? Rav Nachman bar Yitzchak said, because the passuk says “ תתן לו ולא לאורו ” – “You should give to the cohen (to eat) - and not to his fire.”   The asks from a beraisah that says that chametz can become terumah; the gemara explains - " … התם היתה לו שעת הכושר

Shavuos - like one man with one heart

Har Sinai The passuk says in Parshas Yisro: וַיִּסְעוּ מֵרְפִידִים וַיָּבֹאוּ מִדְבַּר סִינַי וַיַּחֲנוּ בַּמִּדְבָּר וַיִּחַן שָׁם יִשְׂרָאֵל נֶגֶד הָהָר “ And they traveled from Rephidim and they came to the desert of Sinai and they camped in the desert and Yisroel camped opposite mountain .” Rashi comments on this passuk : "ויחן שם ישראל" - כאיש אחד בלב אחד אבל שאר כל החניות בתרעומות ובמחלוקת (מכילתא) “ And Yisroel camped there - (this is written in the singular, to teach you that they camped) like one man with one heart, but all the other encampments were with complaints and argument .” ·          Why does Rashi say כאיש אחד בלב אחד – like one man with one heart, why does Rashi not just say like one man? ·          Why was the only camp where there was no machlokess the encampment at Har Sinai ? Machlokess le'shem shamayim The mishna says in Pirkei Avos (5:17) : כל מחלוקת שהיא לשם שמים, סופה להתקיים ושאינה לשם שמים, אין סופה להתקיים. איז