#8- Department store manager: There is absolutely no reason

[Capetowner]

Hi Capetowner,

I'm not entirely sure what you're asking, so please feel free to provide examples of the three types of statements that you are trying to negate.

To just negate a biconditional, you would want a statement that allows one of the terms to occur without the other.

For example, the negation of the biconditional: "You will do well on the LSAT if and only if you study hard" would be:

"It is either possible for you to do well on the LSAT without studying hard or it is possible for you to study hard without doing well on the LSAT."

Of course, it is often easier to negate these more complex statements by simply adding "It is not the case that" before the statement in question. For example, "It is not the case that you will do well on the LSAT if and only if you study hard" is equivalent to the negated statement above and may be easier to figure out and understand.

To negate a mutually exclusive conditional, you would want a statement that allows one of the terms to occur with the other.

For example, the negation of the statement "No doctors are lawyers" would be:

"Some doctors are lawyers."

I'm not quite sure what you mean by your last example (the combo), so please feel free to provide an example for clarification.

Awesome note, wow that clears things up. Just a question on Dave's response above:

On another thread, Dave mentions , the Opposite of "likely (using the spectrum from 0-100)" would be "unlikely" which makes sense, as the opposite of 51-100 is 0-49

Why then when I read Adam's post above, does the opposite of "most" include half? This seems to counter the spectrum approach above

[Jeff Wren]

Hi Capetowner,

While I don't want to speak for Dave, my guess is that he was simply using the word "unlikely" as the negation of "likely" as shorthand to keep things simple. Technically, if "likely" means "probably, or having a greater than 50% of occurring," the logical opposite of that would be anything other than "having a greater than 50% of occurring," which would include something that has exactly a 50% chance of occurring. For example, if there is exactly a 50% chance that I will get heads when I toss a coin, then technically it is not "likely" (i.e. more likely than not) that I will get a heads, since it's equally likely that I will get tails.

As for Adam's post, I believe that he was simply using 50% as an example of something that would be more than a few but would not qualify as most, which would illustrate the Assumption Negation Technique for Answer E. You could also have used a large minority, perhaps 40%, and that would also illustrate the point.

The key to this question is realizing that the argument is making a false dilemma (also known as a false dichotomy) in assuming that it would either be only a few customers who want free gift wrapping or most of them, while ignoring all of the possibilities between those two extremes. Answer E captures this flawed assumption.