Before us is Mishnah 6 of chapter 11 of Nedarim, which deals with partial upholding and partial annulment. A woman vowed not to taste figs and not to taste grapes, and her husband comes to uphold or to annul her vow, but he refers to only part of the vow. The question is what the status of that part is, and what the status of the rest of the vow is.
Two laws are stated here:
Partial upholding - "Kiyem la-te'enim - kiyem le-chulan": If the husband upholds the vow, that is, he wants the vow to remain in force and has no intention of annulling it, and he said so regarding the figs alone, the entire vow stands, including the part she vowed about grapes. From this point on he can no longer annul even the part about the grapes.
Partial annulment - "Hefer la-te'enim - eino mufar ad she-yafer af la-anavim": If the husband annuls the vow, that is, he does not want the vow to take effect, and he said so regarding the figs alone, his annulment accomplishes nothing at all, unless he goes on and annuls the part about the grapes as well.
The source of the distinction in the verse:
The difference between the two laws - that upholding part of a vow upholds all of it, while annulling part of it does not help even for that part until he annuls everything - is derived from the wording of the verse itself. In the language of upholding, the implication is that the husband upholds the vow even when he upholds only part of it, and part is enough to keep the entire vow standing; therefore, even if he upheld only the figs, the whole vow stands. But in the language of annulment the verse says "yafer" - that he must annul the entire vow, and only then does his annulment take effect.
The three opinions in the Gemara:
Rabbi Yishmael: As our Mishnah was taught - upholding part upholds everything, and annulling part accomplishes nothing until he annuls everything.
Rabbi Akiva: Just as we say regarding a sage's release, "a vow that was partially released is entirely released" - that if the sage released part of the vow, the whole vow is released - so too with annulment and upholding: one who annuls part of it has annulled all of it, and one who upholds part of it has upheld all of it. In other words, according to Rabbi Akiva the part is like the whole, both for annulment and for upholding.
A third opinion: The exact opposite - both for annulment and for upholding, the act takes effect only on what he explicitly mentioned. If he annulled only the figs, only the figs are annulled, and if he annulled only the grapes, only the grapes are annulled; and likewise with upholding: what he upheld is upheld, and the other part is not upheld.
The closing clause of the Mishnah:
The Mishnah concludes: "Amrah konam te'enim she-eini to'emet va-anavim she-eini to'emet - harei elu shnei nedarim" - if she said explicitly konam regarding figs, and then said explicitly that she will not taste grapes, this is not one vow that includes two items, but two entirely separate vows, and they are not dependent on one another at all.
In summary: In this Mishnah we learned the distinction between upholding and annulling: upholding part of a vow upholds the entire vow, while annulling part of it accomplishes nothing at all until he annuls all of it, and this distinction is derived from the wording of the verse. We also examined the three opinions in the Gemara - the view of Rabbi Yishmael, which is the view of our Mishnah, the view of Rabbi Akiva that part is like the whole in both directions, and the third opinion that the act takes effect only on what he explicitly mentioned - and the closing clause of the Mishnah, in which it is stated explicitly that a vow expressed in two separate statements is considered two vows.