The second of the three blessings that comprise Birkot Ha'Torah – the series of Berachot recited each morning over Torah study – begins with the words "Ve'ha'areb Na," asking Hashem that we and our offspring should find Torah study enjoyable.
Notably, the first letter of this Beracha is the prefix "Ve" – which means "and." Of course, sentences do not normally begin with the word "and," a conjunction that combines the previous words with the words that follow. Hence, some Poskim concluded that "Ve'ha'areb Na" does not constitute a separate blessing, but rather continues the first blessing ("Asher Kideshanu…Al Dibreh Torah"). According to this view, Birkot Ha'Torah consists not of three Berachot, as it appears, but only of two Berachot. This is the view taken by Rabbenu Tam (France, 1100-1171) and the Tur (Rabbenu Yaakob Ben Asher, Germany-Spain, 1270-1340).
By contrast, the Rambam maintained that these are separate blessings, and he in fact omits the prefix "Ve" from the beginning of the second blessing. In his view, "Ve'ha'areb Na" begins a new blessing, and so the proper text is "Ha'areb Na," without the word "and" at the beginning.
At first glance, we might assume that since the accepted text is "Ve'ha'areb Na," with the prefix "Ve," we follow the view that "Ve'ha'areb Na" continues the first Beracha and does not constitute a separate Beracha. In truth, however, the Bet Yosef (work by Maran Rav Yosef Karo, author of the Shulhan Aruch) writes that the text of "Ve'ha'areb Na" does not necessarily prove one way or the other. The presence of the prefix "Ve" at the beginning of this phrase does not mean that it continues the previous blessing, and it is therefore possible that even according to the accepted text, we have three separate Berachot that form Birkot Ha'Torah.
The practical ramification of this question relates to the response of "Amen" after hearing the first blessing. Just as one may not recite a Beracha in vain, it is likewise forbidden to answer "Amen" in vain. The word "Amen" has great significance; its numerical value is 91, the combined numerical values of the Name of Havaya (26) and the Name of "Ado-nai" (65). One may not randomly say "Amen" anytime he wants. The question thus becomes whether it is appropriate to answer "Amen" after one hears his fellow conclude the Beracha of "Al Dibreh Torah." If "Ve'ha'areb Na" simply continues the Beracha of "Al Dibreh Torah," then one should not answer "Amen," since he did not yet hear a complete Beracha. But if "Ve'aha'areb Na" comprises an independent blessing, then "Al Dibreh Torah" marks the conclusion of a blessing, such that the listener should answer "Amen" at that point.
The Arizal (Rav Yishak Luria, 1534-1572) maintained that Birkot Ha'Torah consists of three separate Berachot, such that "Amen" is warranted even after "Al Dibreh Torah."
The Yalkut Yosef writes that in truth, even if one insists that "Ve'ha'areb Na" merely continues the first Beracha, one may still answer "Amen" to "Al Dibreh Torah." After all, common practice allows proclaiming "Amen" even outside the context of formal blessings. For example, we customarily answer "Amen" at several points during the Hazan's recitation of "Ya'aleh Ve'yabo" (such as after "Zochrenu…Le'Toba"), and also during "Barech Alenu" in the winter. This shows that we do not need to be especially strict when it comes to answering "Amen," and thus regardless of whether we regard "Ve'ha'areb Na" as a separate blessing, it is acceptable to answer "Amen" after "Al Dibreh Torah."
One may, however, question this argument, noting that we answer "Amen" only after hearing a Beracha, or after hearing a prayer. "Al Dibreh Torah" is not a request for anything, and so if it does not mark the conclusion of a Beracha, then it would seem that answering "Amen" is inappropriate. Moreover, if a person seeks to fulfill his Birkot Ha'Torah obligation by listening to his fellow's recitation (such as if he cannot remember if he had recited Birkot Ha'Torah that morning), then answering "Amen" to "Al Dibreh Torah" would constitute a Hefsek (forbidden interruption). In such a case, then, one does not have the option of answering "Amen" unless it can be determined that Halacha follows the opinion which regards "Ve'ha'areb Na" as a separate blessing.
It seems that the accepted custom is to view Birkot Ha'Torah as a series of three separate Berachot, and thus one may and should answer "Amen" to the blessing of "Al Dibreh Torah." We have noted in the past that although we refrain from reciting a Beracha when there is some question whether it is required ("Safek Berachot Le'hakel"), this rule does not apply when there is an accepted custom to recite the Beracha. Even if different opinions exist as to whether a certain Beracha is warranted, we recite the Beracha if this is the established custom. This applies also to answering "Amen." Therefore, since Birkot Ha'Torah are generally seen as a series of three separate blessings, one should answer "Amen" even after "Al Dibreh Torah."
We should note that as this is the accepted custom, Birkot Ha'Torah count as three Berachot toward the total of 100 blessings which a person is required to recite each day.
Summary: The second of the Birkot Ha'Torah begins, "Ve'ha'areb Na," and the prefix "Ve" ("and") might suggest that this continues the previous Beracha, and does not mark the beginning of a new Beracha. In truth, however, the accepted view is that "Ve'ha'areb Na" begins a separate blessing. Therefore, one who hears Birkot Ha'Torah answers "Amen" even after "Al Dibreh Torah," which marks the conclusion of the first Beracha.