Oktzim, Chapter Two, Mishnah Five
1) If one chops up [fruit] for cooking, even if [the chopping had] not been completely finished, it is not regarded as connected.
2) If his intention had been to pickle or to boil it, or to set it on the table, then it is regarded as connected.
3) If he began to take [the pieces] apart, [only] that part of the food which he began to take apart is not considered connected.
4) Nuts that had been strung together, or onions that had been piled together, count as connected.
a) If he began to take the nuts apart, or to strip the onions, they are not connected.
5) [Shells of] nuts and almonds are considered connected [with the edible part] until they are crushed.
Section one: Once one begins to chop up produce in order to cook it, the pieces are no longer considered connected to one another.
Section two: However, if he intends to either pickle, boil or set aside the pieces, then they are considered connected to one another. If one is defiled, then they are all defiled.
It is a bit difficult to understand why or how section two differs from section one. According to Albeck, section two presents cases in which he wants the pieces to stay together until he does something else with them, such as pickle them, put them in a pot or put them in front of those eating. Therefore, they are considered connected. However, in section one he doesn’t care if they stay connected, perhaps because he will cook them separately.
Section three: This refers to section two. Once he begins to take the pieces of the fruit apart from the pile that they were in, the stuff he has taken apart is no longer considered connected. But the parts he has not yet taken apart remain connected.
Section four: Nuts or onions strung together, perhaps to bring them to market, count as connected. But once he begins to take them apart, they are not connected.
Section five: Shells of nuts are connected until they are smashed to get the nuts out. Once they are smashed, they are not considered connected even if he has not yet removed the shells. This is because they no longer protect the nut.