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: