### 50. Let A be a fuzzy set of R, A is a fuzzy number for which of the following membership functions?

### 51. Let A, B be fuzzy numbers, ∪ m , ∩ m denote standard fuzzy union and intersection respectively and, ∪ a , ∩ a denote algebraic sum fuzzy union and algebraic product fuzzy intersection. Which of the following is/are fuzzy numbers? 1. A , with standard complement 2. A ∩ m B 3. A ∪ m B 4. A ∪ a B 5. A ∩ a B

### 52. Let A = (2,4,7) and B=(4,5,6) be triangular fuzzy numbers, ∩ d , ∪ d denote drastic intersection and union respectively. Then which of the following statements is/are correct? 1. A ∩ d B is not normal 2. A ∪ d B is not normal 3. A ∩ d B is a fuzzy number 4. A ∪ d B is a fuzzy number

### 53. Let A = (-1,2,6,8) and B = (2,4,8,10) be trapezoidal fuzzy numbers ∩ b , ∪ b denote bounded difference fuzzy intersection and bounded sum fuzzy union respectively. Then which of the following statements is/are correct> 1. A ∪ b B is a fuzzy number 2. A ∩ b B is NOT a fuzzy number 3. A ∩ m B = A ∩ b B 4. A ∪ b B ⊂ A ∪ m B

### 54. Let A, B be Gaussian fuzzy sets of R such that

### 55. Let A = [-1,4], B = [2,3] and C = [-5, 6]. Which of the following is/are CORRECT? 1. A.C ⊆ A.B 2. B.(A + C) ⊆ A. (B + C) 3. B.(A + C) ⊆ C. (A + B) 4. A.(B + C) ⊂ A.B + (A.C)

### 56. Let A = [5,10], B = [1,2] and C = [-1,1]. Which of the following is/are CORRECT? 1. A - 5B = {0} 2. A = 5B 3. C.(A - 5B) = A - 5B 4. C.A - C.5B = 3(A - 5B)

### 57. Let A = [-4,16], B = [2, 4]. Which of the following is/are INCORRECT? 1. A/B = [-2,4] 2. B.(A/B) = A 3. (B/B) = {1} 4. A ⊂ A.(B/B)

### 58. ∪ m , ∪ a , ∪ b and ∪ d denote fuzzy union with maximum, algebraic sum, bounded sum and drastict-conorms respectively Let A 1 , A 2 , A 3 ∈ F(X). Which of the following is/are TRUE? 1. α A 1 ∪ α A 2 ∪ α A 3 ⊆ α (A 1 ∪ m A 2 ∪ m A 3 ) 2. α A 1 ∪ α A 2 ∪ α A 3 ⊆ α (A 1 ∪ b A 2 ∪ b A 3 ) 3. α A 1 ∪ α A 2 ∪ α A 3 ⊆ α (A 1 ∪ a A 2 ∪ a A 3 ) 4. α A 1 ∪ α A 2 ∪ α A 3 ⊆ α (A 1 ∪ d A 2 ∪ d A 3 )

### 59. ∩ m , ∩ a , ∩ b and ∩ d denote fuzzy intersection with minimum, algebraic product, bounded difference and drastic t-norms respectively Let A 1 , A 2 , A 3 ∈ F(X). Which of the following is/are TRUE? 1. α+ A 1 ∩ α+ A 2 ∩ α+ A 3 ⊇ α+ (A 1 ∩ m A 2 ∩ m A 3 ) 2. α+ A 1 ∩ α+ A 2 ∩ α+ A 3 ⊇ α+ (A 1 ∩ b A 2 ∩ b A 3 ) 3. α+ A 1 ∩ α+ A 2 ∩ α+ A 3 ⊇ α+ (A 1 ∩ a A 2 ∩ a A 3 ) 4. α+ A 1 ∩ α+ A 2 ∩ α+ A 3 ⊇ α+ (A 1 ∩ d A 2 ∩ d A 3 )

### 60. Let A, B be fuzzy sets on R, C = α A and D = α B. Which of the following is/are Correct?

### 61. Let A be a fuzzy set with

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