I am wondering about something. Let's take the example of the bachelor: (1) If X is a man, and (2) if X is unmarried, then (3) X is a bachelor. So in this example, (1) is a necessary condition for (3), and (2) is also a necessary condition for (3). But considered together, if (1) and (2) are both satisfied, can that be considered a sufficient condition? Like in the following example, (4) If X is an unmarried man, then (5) X is a bachelor. (4) is now a sufficient condition for (5). Am I right? My actual question is, is there any other way of stating that (1) and (2) are together sufficient, other than writing them together as one condition, as in (4)? Or can I outright state that "together, (1) and (2) are sufficient for (3)". I haven't taken a logic class, so I don't really know what the "rules" are... (This is for a word problem in my analysis class.) Thanks.