Prove that following properties hold for fuzzy sets

(i) Commutativity (ii) Associativity (iii) Distributivity (iv) Demorgan’s Law

In fuzzy set theory, operations like union, intersection, and complement are defined based on membership functions that assign a degree of membership to each element of the set. The following properties hold for fuzzy sets under these operations:

(i) Commutativity: Commutativity in fuzzy sets states that the order of operations does not affect the outcome. For fuzzy union and intersection, the following holds:

• Fuzzy union: A∪B=B∪AA \cup B = B \cup A
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