1) THE PROHIBITION AGAINST SEPARATING TERUMOS AND MA'ASEROS ON SHABBOS
QUESTION: The Gemara teaches that the Rabanan prohibited separating Terumos and Ma'aseros on Shabbos because the act involves "Tiltul Muktzah," handling Muktzah (Tevel is Muktzah).
Why does the Gemara give this reason? The Gemara in Beitzah (37a) implies that the prohibition is based on a Gezeirah which prohibits one from conducting business transactions (Mekach u'Memkar) on Shabbos. When one sanctifies an object, he thereby transfers its ownership to Hekdesh, a form of business transaction. Separating Terumos and Ma'aseros is prohibited for the same reason. RASHI in Beitzah (9a, DH Ochel v'Holech) mentions another reason for why it is prohibited: one who separates Terumos makes the produce edible, and thus it appears as though he fixes (Metaken) an item. Why does the Gemara here say that separating Terumos is prohibited because the act involves Tiltul Muktzah? (REBBI AKIVA EIGER in GILYON HA'SHAS)
ANSWER: The TOSFOS YOM HA'KIPURIM in Yoma (83b) writes that separating Terumos is prohibited for both reasons. The prohibition of Metaken applies in a case in which one does not pick up or handle the Tevel (such as when the fruit is already separated into two piles and one merely needs to verbally designate one of the piles as the Terumah fruit).
However, if the reason of Metaken applies in every case of separating Terumos, why does the Gemara mention the less-frequent problem of Tiltul?
The Gemara means that although the Isur d'Rabanan of Tiltul is a very strong Isur and is on par with an Isur d'Oraisa (as the TOSFOS YESHANIM writes in Beitzah 3b), nevertheless it is only an Isur d'Rabanan and cannot be what the Torah refers to in the verse "Lema'an Tilmad l'Yir'ah." It goes without saying that the Isurim of Metaken and Mekach u'Memkar are certainly not the subject of the verse. The Gemara's intent is to emphasize that one should not think that Tiltul, which is derived from verses in Nevi'im and is thus forbidden "mi'Divrei Kabalah" (Shabbos 123b), is considered an Isur d'Oraisa. (M. Kornfeld. See Insights to Yoma 83:2.)
2) DOES THE TESTIMONY OF A SINGLE WITNESS EXEMPT A WOMAN FROM YIBUM?
QUESTION: The Gemara discusses whether the testimony of a single witness is accepted to permit a woman to remarry in cases other than that of the Mishnah (87b). The second version of the Gemara asserts that the testimony of a single witness certainly is accepted to allow the woman to do Yibum when he says that her husband died with no children. This is because a single witness is believed more than a woman is believed, and the law is that a woman alone is believed to say that her husband died without children and thereby permit herself to do Yibum (114b). What, though, is the law when a single witness testifies that a woman does not have to do Yibum (for example, he testifies that her Yavam died, or that her husband died before his children died). In such a case his testimony counters the Chazakah that she is permitted to do Yibum. Moreover, the woman herself is not believed to exempt herself from Yibum with such testimony, as the Mishnah later says.
The Gemara inquires whether the single witness should be believed because his testimony is "Avida li'Geluyei" (the truth will eventually become known), or whether he is not believed because, in this case, the woman will not investigate the matter adequately because she prefers to be exempt from Yibum, since she hates the Yavam.
Why does the Gemara ask specifically about the law in this case, in which the single witness testifies against the Chazakah and says that the woman is not obligated to do Yibum? The Gemara should ask the same question about a case in which the single witness testifies that she is obligated to do Yibum, and his testimony counters a Chazakah that she is exempt from Yibum (for example, he testifies that her husband died after his children died). (TOSFOS DH Ki)
(a) TOSFOS, in his first answer, explains that the two questions indeed are the same. The Gemara mentions the question of a witness who attempts to permit the woman to marry without Yibum because it happens to be that this was the question posed as a result of an incident which occurred at the time.
(b) The RAMBAN and other Rishonim suggest that the Gemara intentionally discusses a case in which the single witness attempts to exempt the woman from Yibum. One might have assumed that in such a case, the single witness certainly should be believed, because even if his testimony is wrong and the woman is actually obligated to do Yibum, she transgresses only a Lo Ta'aseh (the Isur of Yevamah la'Shuk) and not an Isur Kares. Furthermore, his testimony is about a matter (the Yavam's death) that is "Avida li'Geluyei." Therefore, the Gemara teaches that the witness nevertheless should not be believed because the woman herself might not have investigated the matter thoroughly.
(c) TOSFOS and the RA'AVAD (cited by the Ramban) suggest another explanation. The reason why a woman is not believed to permit herself to the Yavam (by testifying that her child died before her husband died) is not that she does not investigate the matter thoroughly. Her love for and desire to marry the Yavam is never strong enough to cloud her common sense and entice her to testify that her husband died without strong evidence to that effect. Why, then, is she not believed? She is not believed because the leniency of "Mishum Iguna" does not apply in this case; she will not be in a situation of an "Agunah" if she does not become permitted to the Yavam. Hence, when a single witness testifies that she is permitted to the Yavam, his testimony combined with the fact that a woman investigates the facts for herself provide enough grounds to be lenient to permit her to the Yavam (even when the leniency of "Mishum Iguna" does not apply).
On the other hand, when a woman testifies that she is not obligated to do Yibum, not only is there no reason to apply the leniency of "Mishum Iguna" (since, if she is not believed, she will not be left unable to marry -- she may marry the Yavam), but there is also a suspicion that she will not adequately verify that she is truly exempt from Yibum. Since she presumably hates the Yavam, she is suspected of neglecting to investigate whether she is indeed exempt from Yibum. Her hate can overcome her common sense; the emotion of hate tends to be more powerful than the emotion of love.
Consequently, when a single witness testifies on her behalf, his testimony is not accepted because the additional factor that the woman carefully investigates the facts for herself is not present. For this reason, the Gemara asks what the Halachah is only in a case in which the witness testifies that she is exempt from Yibum.