• Rav Zev Jacobson
Daf 6a
A.  Ba'u minei mi-Rava behemat arnona [lines 4-8]  There are 3 different categories in the law of the firstborn [bekhor]:
1. Man - A firstborn son must be redeemed one month after he is born by giving 5 shekels to a kohen [see Shemot 13:13 and Bamidbar 18:16].  This applies only if neither parent is a kohen or a levi.
2. Livestock - A firstborn cow, goat or sheep that is without a disqualifying blemish [mum] must be offered as a sacrifice.  If it is unfit to be sacrificed, it is given to a kohen to do with as he pleases [Devarim 15:19-23].
3. Donkey - A firstborn donkey must be redeemed by giving its monetary equivalent, or a sheep to a kohen to do with as he pleases.  Otherwise, the owner must break the donkey's neck [see Shemot 13:13:].
            Only the firstborn of the female is considered for all of the above.  Thus, there is no command to redeem the a man's firstborn if his wife has borne children in the past with someone else.  Furthermore, only Jews and their animals can acquire the sanctity of the firstborn.  Thus, an animal that is owned, even partially, by a non-Jew is not subject to the laws of bekhor.  [See Masekhet Bekhorot for a fuller treatment of the laws of firstborn.]
            As recorded by our gemara, Rava was asked: "If one's flocks are subject to arnona [a 10% tax levied by the non-Jewish king] is he obligated in the laws of bekhor?"  In other words, do we consider the 10% to be a levy; or a stake in the livestock?  According to the first option, the non-Jewish king has no share in the animals, he merely exacts a tax, and the owner is obligated in the laws of bekhor.  According to the second option, the non-Jewish king has part-ownership [10%] over ALL the animals.  Therefore, the laws of bekhor do not apply.
B.  Amar R. Yehuda amar Rav ha-motzeh chametz [lines 30-31]  If one finds chametz in his possession on Yom Tov he is required to cover it with a vessel until after Yom Tov when he can dispose of it.  He may not move the chametz as it is muktzeh, having no use on Pesach.  However, we are concerned that he may come to eat the chametz by mistake and, therefore, it must be covered.  Rashi [s.v.Kofeh Alav Et Ha-kli] notes that one does not violate the prohibition against possessing chametz as he has already nullified it [bitul] before Pesach.