diagramming of contrapositives

[hugheshaus]

As I am working through the conditional reasoning drills, I am noticing that I am diagramming the contrapositives slightly different than the answers in the book. For example, on problem #1, the contrapositive was diagrammed S5 ----> R3 with slash through the R3. When I diagram it, I have been putting R3 (with slash through it) < --- S5. Is it important that I diagram it in the direction the book does rather than the way I have been doing it, and if so, why?

[Jeremy Press]

Hi hughes,

We standardize the direction of normal conditional and contrapositive arrows as being left to right. We think that's easier for most folks to read since it fits the direction we read English and since it allows you to "visualize" every conditional and contrapositive relationship in the same standard way (i.e. sufficient condition is always on the left; necessary condition is always on the right).

The way you've reversed the arrow in your contrapositive diagram isn't "wrong," though. You just have to remember in the way you're diagramming it that the term you have on the right side of the arrow is the sufficient condition (and when it occurs the necessary will HAVE to occur), whereas the term you have on the left side of the arrow is the necessary condition (so it can occur whether or not the sufficient condition occurs). As long as you can remember that easily, you can keep diagramming as you are!