Given G = {V, T, S, P} be the phase-structure grammar with V = {0, 1, A, S}, T = {0, 1}, and set of productions P consist of the following: S→ 18;S→ 00A ; A → OA ; A → 0 Show that 1111000 belongs to the language generated by G.
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- Assume that is an associative binary operation on the non empty set A. Prove that a[ b(cd) ]=[ a(bc) ]d for all a,b,c, and d in A.Since by definition a language L over an alphabet A is just a subset of A*, the set of all languages over an alphabet A is the powerset of A*. options:TrueFalseSuppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B. a) the set of sophomores taking discrete mathematics in your school b) the set of sophomores at your school who are not taking discrete mathematics c) the set of students at your school who either are sophomores or are taking discrete mathematics Use these symbols: ∩ ∪
- In a freshman class of 68 high school students, 20 students are taking history, 40 students are takingmath, and 15 students are taking both history and math. Draw a Venn diagram to represent thissituation. Label each part of the diagram clearly.In Exereises 6 and 7, let p, q, and r be the following state- ments: p: I will study discrete structure; q: I will go to a movie; r: I am in a good mood. 6. Write the following statements in terms of p, q, r, and logical connectives. (a) If1 am not in a good mood, then I will go to a movie. (b) I will not go to a movie and I will study discrete structures, (c) I will go to a movie only if I will not study discrete structures. (d) IfI will not study discrete structures, then I am not in a good mood.Let s be a string of length 2 with characters from {0, 1, 2}, and define statements a, b, c, and d as follows:a = “the first character of s is 0”b = “the first character of s is 1”c = “the second character of s is 1”d = “the second character of s is 2”. Describe the set of all strings for which each of the following is true. Attachment