Final answer:
In mathematics, all members of a set share the common characteristic of satisfying the specific membership criteria that define that set. c) Membership criteria is correct answer.
Step-by-step explanation:
The shared characteristic among all members of a mathematical set is Membership criteria. A set in mathematics is a well-defined collection of distinct objects, considered as an object in its own right.
For any given set, there are specific properties or rules - the membership criteria - that determine if an object is a member of that set. Every element in a set must satisfy these criteria, which are distinct and specific to that particular set.
A shared characteristic among all members of a mathematical set is:
Membership criteria
Mathematical sets are defined by their membership criteria, which establish the elements that belong to the set. For example, in a set of even numbers, the membership criteria is that the elements must be divisible by 2. This characteristic sets apart the elements that belong to the set from those that do not.