p.609, icon at Example 2#1.(a) Verify that the following is an equivalence relation on the set of real numbers:aRb → [a] = [b], where [x] is the floor of x.(b) Describe the equivalence classes arising from the equivalence relation in part (a).

Answered: Image /qna-images/answer/a9cb2696-f26d-45c4-b657-5020ed0dcb58.jpg

Answered: p.609, icon at Example 2 #1. (a) Verify…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Exercise 5. Regular Languages This exercise relates to languages of words over the alphabet {a, b}. For a given word w, Jwr| is the number of occurences of the character x in the word, i.e. if abaab, then Jwal W = 3 and wb| = 2. For each the languages below either (i) give a DFA that recognises the language; OR (ii) provide an argument as to why a DFA that recognises the language cannot be produced (a) All words w s.t. wa| > |w6|- (b) All words where the following equality holds: |wa| mod 2 = wo| mod 2
(1) For each of the following languages, say whether it is context-free. If so, write a CFG or draw a PDA (non-mathematically) that generates the language. If not, prove it using the pumping lemma and/or closure properties for CFLS. (a) (b) (c) (d) L = {a" | n > 0}. L = {amb"c{m-n) | m > n} {amb"cm" | m, n 2 0} L = {a"b" cm | m > n} L
3 CNF Step 3Perform step three of converting the following CFG’s into CNF by removingunit rules.3.aV = {S,A,B}, Σ = {a,b}, S = S, R =S →AA →AA |AB |A |B |aBB →BB |Bb |b
a) Define the following concept formally using description logics:A university has a female president, at least 5 vice presidents, all department chairs are professors whose ranks are full, and who have served the university for at least 10 years. b) Suppose we have a knowledge base-- PhD circle-equals [AND GraduateStudent [FILLS :Program doctorate]]-- GraduateStudent squared-subset-or-equals Student Which of the following two sentences is a valid one? Which one can only be entailed?A) [AND Student Male] squared-subset-or-equals StudentB) [AND PhD Male] squared-subset-or-equals Student
Use the Pumping Lemma to show that the the following language over {a,b,c}* is not CF {wct | t ∈ {a,b}* ∧ w is a substring of t}
7. List the ordered pairs in the equivalence relations produced by these partitions of ta.b.c.d.e.f.g. a) {a,b).c.d.le.f.g}. b) (a.b.c.d.ef.lg).
1b) Let A = {aibjck∶0 ≤ i ≤ j ≤ k}. Use the pumping lemma for context-free languages to prove that A is not a context-free language. 1c) Let A = {w#w∶w ∈ {a,b}*}. Use the pumping lemma for context-free languages to prove that A is not a context-free language.
Please, I want a correct solution to all paragraphs. The solution must be in text format and not handwritten Course name: computer drawing
Question For each of the following, determine whether argument is valid. You may use a counterexample or equivalence transformations to justify your answer. (a) P→ q (b) (c) קר :: 79 P→r q→r ¬(pv q) :: r P→r q→r qV¬r :: 19
Please solve complete
Undecidability Prove that the following language is undecidable. L={⟨M⟩|M is a TM and accepts at least one string of the form 1^∗0^∗1^∗} To do so: Describe a reduction from ??? to L Prove correctness of your reduction.

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p.609, icon at Example 2 #1. (a) Verify that the following is an equivalence relation on the set of real numbers: aRb → [a] = [b], where [x] is the floor of x. (b) Describe the equivalence classes arising from the equivalence relation in part (a).