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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
2 and 3
1 and 4
3, 4 and 5
None of the above
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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
2 only
1 and 3
All of the above
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
1, 3 and 4
2, 3 and 4
3 only
4 only
54. Let A, B be Gaussian fuzzy sets of R such that Which of the following statements is/are TRUE? 1. A, B is a fuzzy number for any m1, m2, s1, s2 2. A, B is a fuzzy number iff m1 ∈ [a1, a2], m2 ∈ [b1, b2] 3. A ∩m B is a fuzzy number iff m1 ∈ [a1, a2], m2 ∈ [b1, b2] and m1 = m2 4. A ∪m B is a fuzzy number iff m1 ∈ [a1, a2], m2 ∈ [b1, b2] and m1 = m2
1 only
1, 2 and 3
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)
1 and 2
3 and 4
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