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Artificial Intelligence - Fuzzy Sets

Avatto > > UGC NET COMPUTER SCIENCE > > PRACTICE QUESTIONS > > Artificial Intelligence > > Fuzzy Sets

21. Which of the following is/are TRUE with respect to crisp sets A, B ⊆ X, where X is the universal set?
1. (Ac ∪ B) ∪ (A ∪ Bc) = X
2. (Ac ∩ B) ∩ (A ∩ Bc) = X
3. A ∩ (Ac ∪ B) = A ∪ B
4. A ∪ (Ac ∪ B)c = A

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22. Let A, B and C be crisp sets such that A ⊄ B and B ⊆ C. Which of the following is/are CORRECT?

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23. Which of the following is/are Fuzzy sets for X = {x1, x2, x3, x4}?
A = {(x1,0), (x2,0), (x3,0), (x4,0)}
B = {(x1,1), (x2,1), (x3,1), (x4,1)}
C = {(x1,0.5), (x2,0.4), (x3,0.7), (x4,1.1)}
D = {(x1,-0.2), (x2,0.4), (x3,0.6), (x4,0.1)}
E= {(x1,0), (x2,1), (x3,0), (x4,1)}
F = {(x1,0.1), (x2,0.5), (x3,0.2), (x4,0.07)}

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24. Which of the following is/are crisp sets for X = {x1, x2, x3, x4}?
A = {(x1,0), (x2,0), (x3,0), (x4,0)}
B = {(x1,1), (x2,1), (x3,1), (x4,1)}
C = {(x1,0.5), (x2,0.4), (x3,0.7), (x4,1.1)}
D = {(x1,-0.2), (x2,0.4), (x3,0.6), (x4,0.1)}
E= {(x1,0), (x2,1), (x3,0), (x4,1)}
F = {(x1,0.1), (x2,0.5), (x3,0.2), (x4,0.07)}

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25. Let A, B, C be fuzzy sets of X. Which of the following is/are CORRECT with respect to standard fuzzy union, intersection and complement?
1. A ∪ Ac = X
2. A ∩ (B U C) = (A ∩ B) ∪ (A ∩ C)
3. (A ∩ B)c = (Ac U Bc)
4. A ∩ (A U B) = A

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