Based on the passage, it can be concluded that the author and Broyles-González hold essentially the same attitude toward

Dalaal on February 28, 2020

Reversing all statements

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?

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SamA on February 29, 2020

Hello @Dalaal,

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