Question about Parallel Reasoning Example

[Jkjones3789]

On page 407 of the Logical Reasoning Bible , there is a parallel reasoning question. I was able to get the correct answer, however I have an issue with this statement being called a mistaken contrapositive ....

Jenny will have lots of balloons at her birthday party. There are no balloons around yet s
today is not her birthday.

I would've interpreted it as B --> BP
-B ---> BP
B = Balloons
BP = Birthday Party

Why is this a mistaken contrapostive and not a mistaken negation?

[Steve Stein]

Hi,

Thanks for your question; glad to hear that you were able to get to the right answer. Answer choice (B) has an issue as well, but it is not a mistaken negation:

Jenny will have lots of balloons at her birthday party--but that doesn't mean that every time she's in the presence of balloons it will necessarily be her birthday. Rather, if we were to picture her birthday party, we know that "lots of balloons" would be part of the picture:

Birthday party lots of balloons

lots of balloons Birthday party

The conclusion of this answer does not present a perfect contrapositive either, though. Instead, the conclusion presented is that if there are no balloons around, it must not be her birthday.

balloons Birthday

(This is not valid; maybe it's her birthday, but the balloons have yet to arrive, or maybe her party is on a different day entirely).

I hope that's helpful. This stuff can be tricky, so please let me know whether this is clear--thanks!

~Steve

[Jkjones3789]

So in term of the necessary and the sufficient are there indicators that would have allowed me to draw that conclusion? I thought that it would be Balloons --> Birthday Party ... No balloons ---> no birthday party given me the mistaken negation. I kind of understand but I want it to be a little more solid so I don't make the error again.

[Steve Stein]

Hi,

Thanks for your response. Unfortunately, the test makers seek opportunities to avoid the use of indicators—that allows them to make conditional reasoning more challenging, and to test whether you really understand the underlying concepts. The answer is to think it through carefully: There will be lots of balloons at Jenny's party, so which condition tells you something about the other? The presence of balloons doesn't dictate that it will be her party, but if we're at her party, we know that we will be seeing a lot of balloons. That means that "party" is sufficient (because the sufficient condition is always the one that tells you something else is to take place).

Please let me know whether this clear. Thanks!

~Steve

[Jkjones3789]

Thank you so much. I understand it 100% now. I was getting to dependent on seeing the indicator words and forgot what the conditions actually mean. Thanks again !