Disposal does not only refer to sending something to the garbage. I can "dispose" of a PC under my care by giving it to my brother, for example. In fact, "disposal" and "disposition" share very similar meanings in this regard - check their meanings under Merriam-Webster's Online for reference. The only time I've seen "disposition" used in that way though is in legalese, e.g. wills. More commonly I've seen it used in reference to temperament or character.