Construct a nondeterministic finite-state automaton that recognizes the language generated by the regular grammar
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DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A
- For non empty binary relation R={(a, a),(a, b),(a, e),(b, b),(b, e),(c, c),(c, d),(d, d).(e, e)} on the set A={a, b, c, d, e}, which is the following is true? O Reflexive, Anti-Symmetric O Reflexive O Reflexive, Symmetric, Transitive O Reflexive, Transitive O Reflexive, Symmetric, Anti-Symmetric, Transitive O Reflexive, Anti-Symmetric, Transitive O Reflexive, Symmetric O Transitive O Symmetric O Symmetric, Transitive O Anti-Symmetric, Transitivearrow_forward26 of 40 Consider the Datalog programs P1 (left) and P2 (right) below, which use relations R(A, B) and S(A, B). P1 P2: T1(A) R(A, B). T4(A) R(A, B), S(A, B). T2(A) S(A, B). T3(A) + T1(A), T2(A). Which of the following statements is TRUE about the relationships between relations T3 and T4 defined by P1 and P2, respectively? Note that the commas "," used in the rule bodies to separate the predicates is the same as using AND. Select one: T3 and T4 include the same set of tuples. Every tuple in T3 is also contained in T4, that is, T3 C T4. O None of the other answers, that is, T3 and T4 contain different tuples, in general. O Every tuple in T4 is also contained in T3, that is, T4 C T3.arrow_forward5. Using the following context free grammar give a parse tree for the strings. E → E +T|T T → TxF|F F → (E)\a (a) a+a+a (b) ((a))arrow_forward
- To show that the set of all finite strings over the alphabet {0,1,2} is countable, you would define a bijection f: {0,1,2} - N, where f(A)=0 (remember that A is the empty string), listing strings in string order (with 0<1<2). Under this bijection, the f(201) = Your Answer: Answer Suppose that JA|=29, |B|=20, and |A n B| = 10. What is |A U B|? Your Answer: Answerarrow_forwardFor the binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to b, which of the following statements would be true? R={ (0,4), (1, 1), (1, 3), (1, 4), (2, 1), (2, 2), (3, 2), (4, 4) } where A = {0, 1,2, 3, 4} Select one: O Ris symmetric but not antisymmetric O Ris antisymmetric but not symmetric O Ris both symmetric and antisymmetric O none of these options O Ris neither symmetric nor antisymmetricarrow_forwardLet A be the set of letters in the English alphabet with the usual order. Define ⟨A2, ≤⟩ such that (α, β) ≤ (γ, δ) if either α < γ, or α = γ and β ≤ δ. Show that this is a total ordering and also a well-ordering. Use this to justify that the set of words in a particular dictionary is well-ordered. (You may use α, β, γ, δ, ε, ω.)arrow_forward
- (1.) Let T = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Suppose five integers are chosen from T. Show that it is not true that there must be two integers whose sum is 10 by giving a counterexample. In other words, fill in the blank with five numbers from T, no two of which have a sum of 10. (Enter your answer in set-roster notation.) (2.) Suppose five pairs of similar-looking boots are thrown together in a pile. What is the minimum number of individual boots that you must pick to be sure of getting a matched pair? Why? Since there are 5 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be............? . It follows that if a minimum of............. boots is chosen, at least two must be from the same pair.arrow_forwardALEKS - Christian Seither - Learn X + ● https://www-awu.aleks.com/alekscgi/x/Isl.exe/10_u-IgNslkr7j8P3jH-1BjnuwZGiweF Here are the meanings of some of the symbols that appear in the statements belo means "is a subset of." C means "is a proper subset of." Z means "is not a subset of." Øis the empty set. For each statement, decide if it is true or false. . SETS Identifying true statements involving subsets and proper subsets Statement (11, 13, 15) Jxplanation Check (11, 12, 13, 14, 15} (7,9) Ø (c. d. f. g} = (d, f} (q, r, w) C (q, r, w} True False O 0 O O O Search X hparrow_forwardPlease answer A to C.arrow_forward
- 2) Let K be any Boolean algebra. A useful relation × ≤ y (read as “x precedes y” ) if and only if xy=x. i) ii) iii) a) If K is the Boolean Algebra of subsets of a set S, to what familiar relation on the subsets of S does Correspond? Refer to example 7.1 in page 348 in the textbook b) Use the axioms and laws of Boolean algebra to prove the following properties of ← in an arbitrary Boolean algebra K. Make sure that when you use the axioms or laws, write that down in the proof x < x for all x € K (Reflexive property) If xy and y If x can be defined as the elements of K as follows: y and y x, then x=y (Antisymmetric property) z, then x z (Transitive property)arrow_forwardLet B be a finite set and ⟨?,∗, +, ( ), 0, 1⟩ be a Boolean algebra with corresponding Booleanorder ⟨?, ≾⟩. Prove that the complement of an atom is a maxterm. Please answer with proper Discrete Mathematics formatting and syntaxarrow_forwardConsider the set S = {A, B, C, D}: For each of the following relations on S, determine whether it is a partial order, a total order, an equivalence relation, or none of the above, and in one sentence explain why: a) {(A,B), (B,C), (C,D), (A,C), (B,D), (A,D)} b) {(A,A), (B,A), (B,B), (C,C), (C,D), (D,D)} c) {(A,A), (B,A), (A,B), (B,B), (C,C), (A,C), (C,A), (D,D)} d) {(A,A), (B,A), (A,B), (B,B), (C,C), (D,D)} e) {(A,A), (B,A), (A,B), (B,B), (C,C), (C,D), (D,D)}arrow_forward
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