Unless Equation

[onlywinter]

On page 187, you discuss the Unless Equation and state in a side note that "[o]ne alternative approach to 'unless' statements is to convert unless to 'if not,' and then diagram in the normal conditional fashion." I find this method much more intuitive and applied it to question 9 on page 221. However, I am getting a different answer for this multiple condition question.

Here is my answer using the method mentioned in the side note:
-FE & -DS -> LC
-LC -> FE or DS

Here is your answer on page 226:
-LC -> FE & DS
-FE or -DS -> LC

This method gives the same answer as your Unless Equation does except for scenarios with multiple conditions. In these cases, "&" and "or" end up getting switched.

Would you please explain to me why this is? In addition, which answer is correct and why? Both cannot be right.

[Jonathan Evans]

Hey OnlyWinter!

Great question! Both approaches—the "if not" approach and the Unless Equation™ approach—have the same outcome:

• LC FE & DS
  FE or DS LC

Let's use both methods and see how they lead to this result.

"Unless they find an eyewitness and put the defendant on the stand, they will lose the case."

First Method: The Unless Equation

1. Drop the "Unless" and make the rest of the first phrase into the necessary condition.
   FE & DS
2. Negate the second phrase and make it the sufficient conditon.
   LC FE & DS

Second Method: The "if not" approach

1. Replace "unless" with "if not." Here's where you encountered difficulty: you must "distribute" the negation across the entire condition. You not only negate FE and DS, but you also negate the "and." Remember how "and" becomes "or" when it's negated? This is a formal logical principle, called De Morgan's Law. You must do it whenever you are logically negating a statement if there is an "and" or "or" present. Thus, the sufficient condition becomes "if not FE or not DS."
   FE or DS
2. Just leave the second phrase alone and it becomes the necessary condition.
   FE or DS LC

If the second method above works for you, by all means, go for it! Just remember to do the entire negation on compound statements.

I hope this helps!

[onlywinter]

Great explanation! Thank you for citing De Morgan's laws, as well. I appreciate it!

You may want to include this information in the next edition of PowerScore.

[Dave Killoran]

Great explanation! Thank you for citing De Morgan's laws, as well. I appreciate it!

You may want to include this information in the next edition of PowerScore.

Hi Only,

That concept is mentioned in the books/courses, but I avoid using the DeMorgan's reference simply because so few people know it. Might not hurt to do so, though.

Thanks!

[Katya W]

Hi

So, regarding question #9. I diagrammed correctly, however, when I saw “they will lose the case”, I saw it as a negative, as in “will not win the case”.

Also, I thought that when we have an Unless Equation, we are supposed to negate the sufficient condition. So for that reason also it made sense for me to take “they will lose the case” and transform it into “case won”. Therefore, I diagrammed as follows:

CW= case won; EW=eye witness; DS=defendant on stand

CW —> EW and DS
And
/EW or /DS —> /CW

I feel like my version of the diagram has the same meaning.

It seems I do this a lot, so I’m trying to discuss it whenever I notice I’ve done it, so that I can understand whether I should change my approach, or if what I’m doing still works as long as it makes sense to me and I am consistent.

Please let me know, thank you!

[Adam Tyson]

That works well enough in this case, katya, but I would caution you to be careful about using what we call "polar opposition" when negating statements, because that actually results in creating a False Dilemma. What if there is a third option beside losing or winning, such as a tie? This is sort of like negating the word "all" with the word "none," and leaving out the entire range of possibilities in between. When faced with a statement like "they will lose the case," the safest and most accurate negation is "they will not lose the case." Otherwise, your approach is sound and your diagram is good!

[Katya W]

Thank you Adam! I will try to be more careful about this going forward. I appreciate it!