I wrote this definition of fuzzy sets and fuzzy logic for a college assignment and was wondering if it is correct:
Let a be any ordinary element of the universal superset U and A be a subset of U, and P(a) is a membership function, then:
$$\forall a((a \in U \land A \subseteq U) \iff (0 \lt P(a) \le 1 \rightarrow a \in A))$$
This would read "For all element a, a belongs to the superset U and A is a subset of U, then a also belongs to A if, and only if, P(a) is between the interval [0,1)". Is this a correct way to represent the degree of truth elements of a fuzzy logic set can have?
Edit: fixed the proposition.