Conditional Statements with Multiple Suff Cndtns

[htangri]

Hi, I have read through all 3 powerscore bibles and they've been a tremendous help. However i have a question about conditional statements that contain multiple sufficient conditions.

Example: If A and B then you must have C.

I know that if A and B are present, that automatically triggers C. And I know C can be on its own and does not depend on A and B being present.

However, in this situation, is it still possible to have A be present by itself? Or A be present along with C (and B is not present) ?

[BethRibet]

Hi Htangri,

Yes, A or B with or without C is still possible, absent other information. The critical point is that C is only certain (rather than just possible), if both A and B are present, and that if both A and B are present, than C is no longer just possible, it must be present.

If A is present, B & C are both possible, but not certain.
If B is present, A & C are both possible, but not certain.
If C is present, A & B are both possible, but not certain.

If A & B are both present, then C is certain.
If C is absent, then A or B, but not both can be present (at least one must be absent).

Thanks for the question; I hope this helps!

Beth

[htangri]

Yup that definitely makes it clear. Thanks Beth!!

[htangri]

Hi,
I have another question about a similar situation with a conditional statement containing two sufficient conditons, but this one involves negatives which makes things slightly more complicated and so I just wanted to clear something up.

The statement reads: If M or N is NOT present, then O must be present.
This means that if either M or N is not there, O is automatically present. Via the contrapositive, If O is not present, then M AND N is present. So up until this point everything makes sense to me here (the original statement and the contra).

Which leads me to my question: under these conditions, can we have all three (O,M,N) be present? And whats happens if BOTH M and N are NOT present, does that mean O must be present? can there be a situation where all three of them are NOT present?

[Ron Gore]

Good morning, Htangri!

Let's see if I can help clear this up for you. You're definitely on the right track, and the questions you ask are getting into a more complex understanding of conditional reasoning.

The statement reads: If M or N is NOT present, then O must be present.
This means that if either M or N is not there, O is automatically present. Via the contrapositive, If O is not present, then M AND N is present. So up until this point everything makes sense to me here (the original statement and the contra).

You're exactly right with what you've written so far! Now, for the tough questions:

Under these conditions, can we have all three (O,M,N) be present?

You definitely can have all three variables present. The way to check this is to see whether the presence of any of the variables shows you that any of the other variables must be absent. As you've correctly described above, the sufficient conditions in the original statement and the contrapositive relate to the absence of variables. Since the presence of variables occurs only in the necessary conditions, they do not show you anything.

And whats happens if BOTH M and N are NOT present, does that mean O must be present?

When you have an "or" condition, it means at least one of the two, unless it explicitly states "but not both." So, the full reading of the sufficient condition you describe is "at least one of M or N is absent." Having both M and N absent does not change the fact that the sufficient condition was satisfied as soon as one of them was absent. So, when both M and N are absent, O must be present.

Can there be a situation where all three of them are NOT present?

No, you cannot have all of the variables in this rule absent. The reason for this is that having either or M or N absent requires the presence of O, and having O absent requires the presence of M and N. This type of relationship is not as frequently tested as some others. However, when it is included in a game, it tends to be an important rule. An example that you may want to check out is the Fruit Stand game from December 2001, PT 36.

Please let me know if I can help further!

Ron

[htangri]

Thanks for clearing that up Ron I really appreciate it!! I'd rather not see this on the test but I'll be ready for it if it happens haha!!