Question 24 (17). If L₁ is reducible to L₂ and L₁ D, then L₂ € D. True False
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A: If L1 and L2 are not in D then L1 U L2 is in D
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A: I have given an answer in step 2.
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Q: Question 22 (15). If L₁ is reducible to L2 and L₂ ED then L₁ E D O True O False
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Q: (16). If L₁ is reducible to L2 and L2 € SD then L₁ € SD O True O False
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A: the answer is given below:-
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- Three persons P1, P2, and P3 were invited by their friend F to make some smørbrød (sandwich made of bread, eggs, and tomato) together. To make a portion of smørbrød, three ingredients are needed: a slice of bread, a slice of tomato, and a slice of an egg. Each of these persons P1, P2, P3 has only one type of each of the ingredients: person P1 has slices of bread person P2 has slices of tomato; person P3 has slices of egg. We assume that persons P1, P2, and P3 each has an unlimited supply of these ingredients (i.e., slices of bread, slices of tomato, slices of egg), respectively. Their friend F, who invited them, also has an unlimited supply of all the ingredients. Here is what happens: the host F puts two random ingredients on the table. Then the invited person who has the third ingredient picks up these other two ingredients, and makes the smørbrød (i.e., takes a slice of bread, puts on it a slice of tomato, and puts on top a slice of egg), and then eats the smørbrød. The host of…Prove the following statement first using proof by contrapositive then proof by contra-diction: For any two integers a,b if a ∗ b ≥ 20 then a ≥ 5 or b ≥ 5.3. Consider the rules Age > 40 ⇒ Donor and Age ≤ 50 ⇒￢Donor. a. Are these two rules mutually exclusive? b. Are these two rules exhaustive?
- Which of the following statements are true given A* (admissibility and consistency of heuristics ] ? The heuristic function h[n] is called admissible if h[n] is never larger than h*[n], namely h[n] is always less or equal to true cheapest cost from n to the goal. If the heuristic function, h always underestimates the true cost [h[n] is smaller than h*[n]), then A* is guaranteed to find an optimal solution. When h is inconsistent, it can not be admissible. If h is consistent and h[goal)=0 then h is admissible A* is complete and optimalQuestion 43 The correct statements are: If L₁ is reducible (regardless of the complexity of the reduction) to L₂ and L₂ is NP-hard, then L₁ m also be NP-hard. If L₁ is reducible (regardless of the complexity of the reduction) to L₂ and L₁ is NP-hard, then L₂ m also be NP-hard. If L₁ is polynomially reducible to L2 and L₂ is NP-hard, then L₁ must also be NP-hard. If L₁ is polynoimially reducible to L₂ and L₁ is NP-hard, then L2 must also be NP-hard.Question 46 The correct statements are: If L is finite, then ¬L must be in P. If L is finite, then ¬L must be in NP. If L₁ and L2 are finite, then L₁ U L₂ must be in P. If L₁ and L₂ are finite, then L₁ U L₂ must be in NP.
- A safe has 5 locks v,w,x,y,z all of which must be unlocked for the safe to open The keys to the locks are distributed among five executives in the following manner: i. A has keys for locks v and x; ii.B has keys for locks v and y; iii.c has keys for locks w and y; iv.D has keys for locks x and z; v.Ehas keys for locks v and Z. vi.Find all the combinations of executives that can open the safe. Write an expression vii.f(A,B,C,D,E)which specifies when the safe can be opened as a function of which viii. Executives are present.Question 5How would you describe the relationship between x and y in the following? da 6 4 2 10 DOCTO LIFE parabolic positive negative no relationship to ..0 total_bill 40 And
- Show that each of the following restrictions of SAT are NP-complete: a) Each clause contains three or fewer literals and each variable appears in three or fewer clauses. b) Each clause contains exactly three literals and each variable appears in four or fewer clauses.Propositions and quantifiers Let x, y ∈ {2, 3, 4}. For the following propositions provide aproof or counterexample to the statements below:•P0(x, y): x < y•P1(x, y): both x and y are even•P2(x, y): x ×y > 7•P3(x, y): x is even and x + y is a multiple of x.•P4(x, y): x ̸= y (a) for all propositions P in P0, . . . , P4,[∃x ∀y P ] →[∀y ∃x P ] (b) for all propositions P in P0, . . . , P4,[∀x ∃y P ] →[∃y ∀x P ]3