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The image you uploaded contains two questions regarding fuzzy sets and operations on them. Let's break them down step by step.

### Q.01:
Two fuzzy sets \( \tilde{G} \) and \( \tilde{H} \) are given:
- \( \tilde{G} = \{(A,1), (B,0.65), (C,0.5), (D,0.35), (E,0)\} \)
- \( \tilde{H} = \{(A,0), (B,0.35), (C,0.5), (D,0.65), (E,0)\} \)

#### Calculations:
The operations here involve:
- \( \cup \): union
- \( \cap \): intersection
- \( \bar{G} \): complement of \( G \)
- \( \bar{H} \): complement of \( H \)
- \( \oplus \): maximum or t-conorm (sum-based combination)
- \( \odot \): minimum or t-norm (product-based combination)

For each operation, you compare the membership values of corresponding elements in \( \tilde{G} \) and \( \tilde{H} \).

### Q.02:
Two fuzzy sets \( \tilde{M} \) and \( \tilde{N} \) with a universal set \( U = \{1, 2, 3, 4, 5, 6\} \) are given:
- \( \tilde{M} = \{(1,0.3), (2,0.1), (3,0), (4,0.9), (5,0.1)\} \)
- \( \tilde{N} = \{(1,0), (2,0.6), (3,0.5), (4,0), (6,0.45)\} \)

#### Calculations:
Again, operations like union, intersection, complement, and specific t-norm or t-conorm calculations need to be performed for each pair of fuzzy sets.

Would you like to go over the step-by-step solution for each of the operations (e.g., union, intersection, complement, etc.)?

Let me know if you have any questions! Here are some related topics to explore:

1. What is the difference between fuzzy set union and intersection?
2. How are fuzzy set complements calculated?
3. What are t-norms and t-conorms in fuzzy logic?
4. How does the universal set affect fuzzy set operations?
5. What are the practical applications of fuzzy set operations?

### Tip:
Fuzzy set operations rely heavily on max-min logic rather than traditional binary operations, so pay close attention to how membership values are combined based on the type of operation.

Two fuzzy sets and their operations were given. The sets are provided along with operations like union, intersection, complement, and t-norm/t-conorm calculations. Users need to calculate these operations for two sets of fuzzy sets across different examples.

Learn how to perform fuzzy set operations, including union, intersection, and complement, on given sets. This problem also includes t-norm and t-conorm calculations with step-by-step solutions. Ideal for advanced mathematics students.

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