Reading diagrams Conditional Possibilities VS Certainties

[salgado145]

This drill is in the Lesson 2 homeowork powerscore
I don't seem to understand the diagram
Statement:
H
or -----> K------> L
J

if H does not occur what:

Must be True: J could occur, J cannot occur, K occurs , k cannot occur , L occurs, L cannot occur
* I thought that if H doesn't occur J has to occur and then KL have to occur why is the answer key saying that K and L doesn't occur
Could Be true
Cannot be true:

If K does not occur what:
Could be true: L occurs , L doesn't occur
*how can L occur . If Not having K means no L
im confuse. Thank you in advance

[Jeff Wren]

Hi salgado,

Based on your question/comment, it appears that your understanding of conditional reasoning may be confused. Given how important conditional reasoning is, you will want to correct this right away before proceeding with other drills and LR questions.

The first thing that you will want to do is to go back and reread the discussion of conditional reasoning in lesson two as well as the chapter included in the additional reading (where this drill is found). Be sure to start at the very beginning and take your time to make sure that you fully understand how conditional reasoning works. I'd also recommend watching the lesson 2 concept recap video in the lesson 2 homework online.

For now, the key thing to understand is that the sufficient condition guarantees the necessary condition, but not the other way around.

Here is a simple example that is true in the "real" world:

If you live in Kansas, then you live in the United States.

Living in Kansas indicates (guarantees) that you live in the United States. "Living in Kansas" is the sufficient term, and "living in the US" is the necessary term.

We would diagram this with the sufficient term at the beginning of the arrow and the necessary at the end, such as:

LK -> LUS

The arrow visually shows that you can always "go" from the sufficient to the necessary.

Of course, living in the United States does not guarantee that you live in Kansas. The important thing to understand is that the necessary term (living in US) can happen without the sufficient term (living in Kansas).

Also, if you do not live in Kansas, that does not guarantee that you do not live in the United States. We call this logical error a Mistaken Negation.

In the drill, "H or J" is the sufficient condition. This means that if "H" happens or "J" happens (or both), then we know that "K" happens, which then tells us that "L" happens. Neither H nor J has to occur.

What you may be confusing is an either/or statement by itself (and not as part of a sufficient condition).

For example, if a statement reads:

Either A or B must occur.

That means that if A doesn't occur, then B must occur (and if B doesn't occur, then A must occur.)

In your second question, not having K tells us nothing about L. Remember that the necessary can occur without the sufficient, just like not living in Kansas doesn't tell us whether you live in the United States. We don't know either way.

[salgado145]

H
or -----> K------> L
J

Should I do the contrapositive of the diagram ? Or It is not necessary

Thank you for the explanation

[salgado145]

what throws me off is that when the question ask If K doesn't occur in the diagram
H
or -----> K------> L
J
I treat K as a sufficient (triggers) and L as a necessary (require)
In the answer key of the workbook it states that L doesn't occur and L does occur . I understand how L occurs but not how L doesn't occur . Thank you

[Dave Killoran]

H
or -----> K------> L
J

Should I do the contrapositive of the diagram ? Or It is not necessary

Thank you for the explanation

In the early days of studying we recommend you look at it--draw it out if needed--so you know what it is and get used to seeing it.

Later on, in most cases you won't need to draw it--you should know it by heart, automatically.

Thanks!

[Dave Killoran]

what throws me off is that when the question ask If K doesn't occur in the diagram
H
or -----> K------> L
J
I treat K as a sufficient (triggers) and L as a necessary (require)
In the answer key of the workbook it states that L doesn't occur and L does occur . I understand how L occurs but not how L doesn't occur . Thank you

K is a sufficient condition here as far as L, so if K does not occur, we know nothing about L. Think about this statement:

• "If I am rich, then I am happy." Let's say someone isn't rich. What do we know about their happiness then, based on that? Nothing at all.

In more abstract terms, when a sufficient condition doesn't happen, it tells us nothing about what happens to a necessary condition. When a necessary condition does not happen, then we know the sufficient condition cannot occur. So which condition isn't happening makes a big difference.

Thanks!

[salgado145]

everything is clear thank you !