Hang in there, akatormubarez!
You are not alone in having trouble getting comfortable with conditional reasoning. The language and inferences are not necessarily intuitive. One of the areas in which people have the greatest trouble initially is improperly inferring that they know more than the relationships allow.
The key to conditional reasoning diagrams such as the drills on pages 2-58 and 2-59 is organization. Let's look at the one you highlight, the statement in #3 that:
H
or
K
L
J
Here, the presence of
either H
or J is a sufficient condition showing that K is present. K is sufficient to show you L is present.
You had trouble with the drill, "If H does not occur, what:" Since H is a sufficient condition, being told "not H" does not get you into a contrapositive. Only the necessary condition, once negated, becomes a sufficient condition. To think that the absence of your sufficient condition shows you something else is a Mistaken Negation. Instead, the absence of the sufficient condition just means the rule is not applicable.
So, when you are told not "not H," you can't infer anything. In this case, that means you don't know the status of J, K or L. The fact that J is part of a compound sufficient condition with H doesn't mean that the absence of H tells you anything about J. Remember, the absence of a sufficient condition does not show you anything definitive.
That is why the solution to this drill was that each of J, K and L could be present, but they also could be absent. Don't count as an error your inclusion of "not H" for the must be true items, or your inclusion of "H" for the cannot be true. You're right on both fronts if told that H does not occur. Those responses weren't included because they aren't so much inferences as restatements of "H does not occur."
In terms of the actual questions you missed, I recommend two things. First, make sure you've memorized the lists of sufficient and necessary condition indicators, so that you can help yourself recognize conditional reasoning in stimuli.
Next, make sure that you understand the
relationship created by conditional language. The presence of the sufficient condition, without anything else, is enough to show you that the necessary condition absolutely must also be the case. In the stimuli, look for what you are shown that the stimulus implies should help you understand something else. This is the sufficient condition. What you are supposed to also know based on that is the necessary condition.
In this drill, being shown H would have told you that K was present, which would show you L was present. Same thing with being shown J. The only two ways you would get into a contrapositive would be if they showed you that what was required to be present wasn't, so "not L" or "not K."
Please let me know if this helps.
Ron
I am certain that my failure to grasp this concept is what is inhibiting my ability to get the correct answers. Help!