I understand this simple set theory and the union of sets perfectly. The problem is the meaning of English words. I understand the words "not prohibited " to equal "is permitted" or conversely "not permitted" to be the same as "is prohibited" so these are two identical ways to describe this pair of disjoint sets. Only differenc is which gets the "not." I. e. Not X is is disjoint from X and X is disjoint from not X; and their union is everything, at least in their domain.Billy T, please don't use mathematical terms you do not understand.
Two sets are said to be "disjoint" if they have no common elements. The set of "all things prohibited" is disjoint from the set of "all things not prohibited", quite obviously. I cannot see that the set of "all things NOT prohibited" is in any way distinct from the set of "all things permitted". Therefore the latter pair cannot be disjoint
I certainly agree. In fact if their union is the null set, there is nothing permitted that is also possible! - A strange state of affairs: You are only permitted what is impossible!I would also say that the set of "all things permitted" is not disjoint from the set of "all things possible"...
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