When we have a compound all statement such as A -> B & C and we want to reverse it to some, do we convert the and to or? Meaning does it become B & C some A or B or C some A?
Reply
Create a free account to read and
take part in forum discussions.
I think I can explain it better if I use an example.
All basketball players (BP) are tall (T) and athletic (A). BP - - - - - - - > T and A
All is a quantifier word, but our conditional reasoning also applies. Therefore I can make a contrapositive. In this case, the "and" becomes "or." not T or not A - - - - - - - -> not BP
I don't think that is what you are asking about, but I want to make it clear that there is a difference between contrapositives and reversing a quantifier statement. To your question:
For this purpose, we can safely assume that some basketball players exist. We would not turn it into an "or" statement. We can conclude the following.
T and A - - some - - BP T - - some - - BP A - - some - - BP
