Sufficient and Necessary Problem Set #5

[avengingangel]

In questions 3 and 5 on page 223, I would appreciate explanations for the diagrams/meaning of the following conditional statements. I am not understanding how the book is getting the diagrams it is, after applying the Unless Equation.

Extremely similar situation in #5, answer choice (C) on the same page...

"No politician is censured unless he or she is known to be involved in a serious scandal."

1) *Sees 'Unless'* "Ohh..let's do the Unless Equation! Wee! I am very familiar with this technique so this won't be a problem at all!"
2) What comes after "unless" become nec. condition, "He or she is known to be involved in a serious scandal" modified by "No": ~scandal
3)Negate remaining term and it becomes suf. condition, "Politician is censured" negated becomes politician Avoids Censure: AC
4) So, the lovely diagram is: AC ~scandal ; contrapositive: scandal ~AC

This question's stimulus is diagrammed as: scandal ~RE and ~AC
Contrapositive (although not written out in answer key): RE or AC ~scandal, which can be written as:
RE ~scandal
AC ~scandal

So, I'm not understanding why I shouldn't pick this answer since this stimulus contains a conditional relationship, and this is a Must Be True question stem (besides the obvious fact that A is the correct answer). I should be looking for the Repeat form or contrapositive in the answer choices, right? That's what I feel I am doing here. Is there something wrong with my diagramming? The only thing that does seem 'fishy' about choosing this as the correct answer is that the diagram for its contrapositive, scandal ~AC, does that reflect that of/agree with the stimulus' diagram, scandal ~RE and ~AC. I just feel that this type of question was not addressed in the book up to this point, and so don't feel equipped with a true reason/rule as to why that's the case (that it's wrong).

Any insight would be so helpful!! Thank you!!!!!

[Dave Killoran]

Ok, this is the same situation as #3. You are attempting to apply two mutually exclusive processes to this sentence. Here's how the Unless Equation works here:

• (C) No politician is censured unless he or she is known to be involved in a serious scandal.
  
  Step 1: unless he or she is known to be involved in a serious scandal:
  
  Sufficient condition "he or she is known to be involved in a serious scandal"
  
  Step 2: The remainder is negated (so the "no" is dropped) and becomes the sufficient:
  
  "politician is censured" "he or she is known to be involved in a serious scandal"

As noted in the book, this is then the Mistaken reversal of a portion of the first sentence.

Please let me know if that helps. Thanks!