Which of the followings is not a valid property over two fuzzy relations R̃…

Important λ-cut properties

For fuzzy sets ~R , ~S

(R~∪S~)λ​=R~λ​∪S~λ​

✔ True

2️⃣ Intersection property

(R~∩S~)λ​=R~λ​∩S~λ​

✔ True

3️⃣ Monotonicity propertY

0≤β≤λ≤1

R~λ​⊆Rβ​

✔ True (higher α-cut → smaller set)

4️⃣ Complement property
For α-cuts, complement does NOT preserve equality generally:

So this statement becomes the invalid property.

Therefore

Options A, B, D → valid
Option C → not valid