In this question, I am given two premises. My job is to form a conclusion given these two premises. The following information is from the actual question:

"Premise: All of the Georgians are home owners.
Premise: None of the home owners are job hoppers.
Conclusion: None of the Georgians are job hoppers [Actual answer]."

I responded by saying "Not all of the Georgians are job hoppers." How is it that the logical opposite of "all of the Georgians" has become "none of the Georgians"? I thought that the logical opposite of "all" is "not all".


Matt

Here's the diagram -- I'm hoping it will make this clearer.

G -> HO (If Georgian, then HomeOwner)
HO -/-> JH (If HomeOwner, then NOT job hopper)
Therefore
G -/-> JH (Therefore, if Georgian, then NOT job hopper)

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