The Halacha establishes that the prohibition of Borer applies also to mixtures in which both components are edible, but one is not desired. The undesired component becomes “relative P’solet.” This Halacha is brought by Tosafot (Shabbat 74), Rambam (Shabbat 8:13) and Maran (319:4).
The conventional understanding would be that such a mixture has the same Halacha as a mixture containing inedible P’solet (waste). That is, one must select and remove the food that he desires and leave the relative P’solet. However, careful analysis of the Rambam’s language reveals a big Chidush and leniency. He says “Borer Ha’ehad Min Ha’ehad,” implying that it doesn’t matter which element is selected. This is how Rabbi David Aramah and the Meirat Sefer () understands the Rambam.
The Shulhan Aruch quotes the Rambam verbatim, but the Rema adds a gloss (listen to audio for exact citation), specifying that the undesired food must remain. The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) explains that the Rema is teaching that one must always select the desired food. Thus there is a Machloket how to understand the Rambam. The Be’ur Halacha (Rav Yisrael Meir Kagan of Radin, 1839-1933) writes that because this Machloket touches on an Isur D’oraita (Torah prohibition), one must be stringent.
Even when a mixture contains two foods, one must always select and remove the food which he desires.