Artificial Intelligence - Fuzzy Sets

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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)

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Option : B
Explanation :

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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)

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Option : A
Explanation :

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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)

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Option : D
Explanation :

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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)

Answer
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Option : C
Explanation :

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

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Option : C
Explanation :

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