Brachos 6:8-7:1

Brachos 6:8

If a person ate figs, grapes or pomegranates (as well as the other special species for which Israel is renowned), Rabban Gamliel says he recites three brachos afterwards (i.e., one must bentch). The Sages say he recites one bracha that contains the ideas of the three brachos. (This is our practice.) Rabbi Akiva says that one would recite three brachos (bentching) after any meal, even if it was only boiled vegetables. If one drank water as a beverage (as opposed to, say, swallowing a pill), one recites the bracha of shehakol; Rabbi Tarfon says one should recite Borei nefashos. (Our practice is recite shehakol before and Borei nefashos after.)

Brachos 7:1

Three who have eaten together must join together for bentching. (The group is called a “zimmun.”) If one of them ate demai (doubtfully-tithed produce), first tithe from which terumah had been taken, or second tithe or sanctified food that had been redeemed, he may join in the zimmun for bentching even though his food was problematic in some way. A waiter who ate at least an olive-sized portion from the food may also join the zimmun, as may a Samaritan (who is of quasi-Jewish status). If one ate food from which tithes were definitely not taken, first tithe from which terumah had not been taken, or second tithe or sanctified food that had not been redeemed, he may not join in the zimmun. Similarly, a waiter who ate less an olive-sized portion of the food and a non-Jew may not join the zimmun.