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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
1 and 2
3 only
2 and 3
1 and 4
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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?
A ⊄ C
A ∩ C ≠ Φ
None of the above
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)}
A, B, C and D
D, E and F
A, B, E and F
C, D and F
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)}
A, B and E
B, E and F
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
1, 2 and 3
1, 3 and 4
2, 3 and 4
3 and 4
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