Why is it that B is correct but not A? Are they not the exact same statements build with different logic? If I take the line If not A then some not C, it should be the same as when its inverted as If C then some is A
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Keep in mind that there is no such thing as a contrapositive for quantifier statements. The contrapositive is a concept that applies exclusively to sufficient and necessary statements. It seems that you are treating a quantifier statement as if it had sufficient and necessary conditions, which is a pretty common error.
not A --- some --- not C
You are attempting to reverse and negate these terms. This is the proper protocol for a contrapositive, but we cannot do that here. However, it is possible to reverse a "some" statement. Based on the diagram above, we can also conclude this:
not C --- some --- not A
I would call this a "reversal," rather than a contrapositive in order to avoid confusion.
What you were trying to do here would be perfectly accurate if we were dealing with a conditional statement.
not A ---> not C C ---> A
Mikebuck89June 3, 2020
Thank you Sam - This became much more clear when I got tot the next lesson on Qualifiers!
