Logical reasoning 3rd edition pg 468

[elizabeth.baber]

Hi,

Can someone explain the explanation provided on pg 468 of the 3rd edition logical reasoning book. The question is on the previous page, I don't understand the explanation given for why "B" cannot be inferred.

thanks

[ohthatpatrick]

Let me see if I can take it out of the abstract by putting some familiar names to it.

Let's go back to Romney vs. Obama as our two candidates.

Let's say that some of Obama's supporters think that we should stop Iran from developing nuclear weapons at any cost.

And ALL of Romney's supporters think that we should stop Iran from developing nuclear weapons at any cost.

(B) is saying, "Some Romney supporters have NOTHING in common with ANY Obama supporter."

That means that there are some people supporting Romney who have a list of issues they care about, and NOT ONE Obama supporter agrees with a single issue on that list."

Well that's impossible!

Every Romney supporter has "no nuclear Iran" on his/her list.

And we know that at least one Obama supporter agrees with that issue.

So every Romney supporter could find AT LEAST one Obama supporter who feels the same way about AT LEAST one issue.

All Romney supporters are guaranteed to agree on at least one issue with the Obama supporters who similarly are concerned about "no nuclear Iran".

The true version of (B) would read:
"ALL voters who prefer Candidate B do share at least one common concern with at least one voter who prefers Candidate A."

or ... All Romney supporters share at least ONE common concern with at least SOME Obama supporters.

Let me know if it still doesn't make sense. It's just really tricky "at least + at least + at least" language in (B). You sometimes need to try to contradict or rephrase tricky sounding statements to get a better sense of what they're saying.

For me, the easiest way to understand and think about (B) is
"Some supporters of Candidate B have absolutely NOTHING in common with ANY supporter of Candidate A."

Hope this helps.