The Voice and Set Theory
The expression "Not all members of set N have characteristic r, but all elements with characteristic r are in set N" can be represented with standard set notation as follows.
1. There exist some elements in N that do not have characteristic r. Using the "∃" symbol, to denote "there exists", and the "∉" symbol, which denotes "not an element of."
∃x ∈ N : x ∉ R
This reads as "There exists an element x in N such that x is not an element of R."
2. For the second part, all elements with characteristic r are in set N:
This means that every element in set R is also in set N. This can be represented using the subset symbol "⊆."
R ⊆ N
This reads as "R is a subset of N," meaning every element in R is also an element in N.
3. So, combining both statements:
∃x ∈ N : x ∉ R and R ⊆ N
This expresses that not all members of set N ("No voters") have characteristic r ("racism"), but all elements with characteristic r ("racism") are in set N ("No voters").
Not all "no" voters are racist, but all racists are "no" voters.