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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)
1 and 2
2 and 3
3 and 4
4 only
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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)
1, 2 and 3
2 and 4
58. ∪m, ∪a, ∪b and ∪d denote fuzzy union with maximum, algebraic sum, bounded sum and drastict-conorms respectively Let A1, A2, A3 ∈ F(X). Which of the following is/are TRUE? 1. αA1 ∪ αA2 ∪ αA3 ⊆ α(A1 ∪m A2 ∪m A3) 2. αA1 ∪ αA2 ∪ αA3 ⊆ α(A1 ∪b A2 ∪b A3) 3. αA1 ∪ αA2 ∪ αA3 ⊆ α(A1 ∪a A2 ∪a A3) 4. αA1 ∪ αA2 ∪ αA3 ⊆ α(A1 ∪d A2 ∪d A3)
2, 3 and 4
1, 3 and 4
1, 2 and 4
59. ∩m, ∩a, ∩b and ∩d denote fuzzy intersection with minimum, algebraic product, bounded difference and drastic t-norms respectively Let A1, A2, A3 ∈ F(X). Which of the following is/are TRUE? 1. α+A1 ∩ α+A2 ∩ α+A3 ⊇ α+(A1 ∩m A2 ∩m A3) 2. α+A1 ∩ α+A2 ∩ α+A3 ⊇ α+(A1 ∩b A2 ∩b A3) 3. α+A1 ∩ α+A2 ∩ α+A3 ⊇ α+(A1 ∩a A2 ∩a A3) 4. α+A1 ∩ α+A2 ∩ α+A3 ⊇ α+(A1 ∩d A2 ∩d A3)
60. Let A, B be fuzzy sets on R, C = αA and D = αB. Which of the following is/are Correct?
1 and 3
1 and 4
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