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Discrete MathematicsFor any sets A and B, prove that (i) (A ∪ B)' = A' ∩ B' (ii) (A ∩ B)' = A' ∪ B'201914mDiscrete MathematicsWhich of the following two sets are equal? (i) A = \{1, 2\} and B = \{1\} (ii) A = \{1, 2\} and B = \{1, 2, 3\} (iii) A = \{1, 2, 3\} and B = \{2, 1, 3\} (iv) A = \{1, 2, 4\} and B = \{1, 2, 3\}20222mFormal Language & Automata TheoryWhich of the following statements is/are False? A. For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine. B. Turing recognizable languages are closed under union and complementation. C. Turing decidable languages are closed under intersection and complementation. D. Turing recognizable languages are closed under union and intersection. (i) A and D only (ii) A and C only (iii) B only (iv) C only20212mDesign and Analysis of Algorithms Which one of the following statement is correct? (i) If A \le_p B and B \in P then A \in P (ii) If A \le_p B and $A otin P then B otin P$ (iii) If A \le_p B and B \le_p C then A \le_p C (iv) All of these20222m
PreviousThe statement (\sim P \leftrightarrow Q) \land \sim Q is true, when (i) P : True, Q : False (ii) P : True, Q : True (iii) P : False, Q : True (iv) P : False, Q : FalseNextWhat is the induction hypothesis assumption for the inequality m! > 2^m where m \ge 4? (i) For m=k, k+1! > 2^k holds (ii) For m=k, k! > 2^k holds (iii) For m=k, k! > 3^k holds (iv) For m=k, k! > 2^{k+1} holds
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