Sets operations For cach of the following theorems, acceptable if you choose to use Venn diagrams as part of your explanations. Formal proofs are not required. cither show that the theorem is true or disprove the thcorem. It is 1. Theorem 2 Let U be a universe. Fon all

Sets operations For cach of the following theorems, acceptable if you choose to use Venn diagrams as part of your explanations. Formal proofs are not required. cither show that the theorem is true or disprove the thcorem. It is 1. Theorem 2 Let U be a universe. Fon all

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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Assume that ∀x∃yP(x,y) is true and that the universe id true for x and y is non empty. Which of the following is true ? ∃x∀yP(x,y) and ∃y∃xP(x,y) . Prove your answer either using regular proof in the natural language or by giving a formal inference . In that latter case u may need to use existential rules of inference .
Q.)Solve a & b and explain a. Why do we use DNF in Boolean Algebra Group of answer choices (i) To reduce the Boolean expression to a simplified format (ii) To group common terms in a Boolean expression (iii) To show that a truth table can be represented in Boolean Algebra (they are universal) (iv) Because we like Boolean expressions because we can solve them. b. The grouping of terms in a k-map is done using Group of answer choices (i) Grey Codes (ii) Encryption (iii) Boolean equivalence codes (iv) Karnaugh Codes
Prove each of the following statement, or give a counterexample: A* search with a heuristic which is admissible but not consistent is complete.
correct and detailed answer will be upvoted else downvoted. For a variety of a decent numbers a, one discovered that the amount of approximately two adjoining components is equivalent to x (for example x=ai+ai+1 for some I). x had ended up being a decent number too. Then, at that point, the components of the exhibit a were worked out in a steady progression without separators into one string s. For instance, assuming a=[12,5,6,133], s=1256133. You are given a string s and a number x. Your undertaking is to decide the situations in the string that compare to the neighboring components of the cluster that have total x. In case there are a few potential replies, you can print any of them. Input :The primary line contains the string s (2≤|s|≤5⋅105). The subsequent line contains an integer x (2≤x<10200000). An extra imperative on the input: the appropriate response consistently exists, i.e you can generally choose two nearby substrings of the string s so that in the event that…
2) (L2) Prove using laws of logic that the conditional proposition (p ∧ q) → r is equivalent to (p ∧ ¬ r) →¬ q. 3) (L3) Show that the converse of a conditional proposition p: q → r is equivalent to the inverse of proposition p using a truth table. 4.1) (L4) Show whether ((p ∧ (p→q)) ↔ ¬p) is a tautology or not. Use a truth table and be specific about which row(s)/column(s) of the truth table justify your answer. 4.2) (L4) Give truth values for the propositional variables that cause the two expressions to have different truth values. For example, given p ∨ q and p ⊕ q, the correct answer would be p = q = T, because when p and q are both true, p ∨ q is true but p ⊕ q is false. Note that there may be more than one correct answer. r ∧ (p ∨ q) (r ∧ p) ∨ q
Prove f(n) = n3 - (n2 log2 n) + 2n f(n) ∈ O(n3) by giving the constants (c, n0) and arguing that your constants hold as n goes to infinity by either "chaining up", "chaining down", carefully treating the inequality as an equality and doing some algebra, or even weak induction. Also, what is the minimum val4ue for c (in the definition of O() ) forj this problem and is it an exclusive or inclusive minimum/bound.
Correct answer will be upvoted else downvoted. Computer science. change b1,b2,… ,bn permits a stretch [l′,r′] to holds its shape if for any pair of integers (x,y) with the end goal that l′≤x<y≤r′, we have bx<by if and provided that ax<ay. A change b1,b2,… ,bn is k-comparative if b permits all stretches [li,ri] for all 1≤i≤k to hold their shapes. Yuu needs to sort out all k-comparable changes for Touko, however it turns out this is an exceptionally hard undertaking; all things considered, Yuu will encode the arrangement of all k-comparable stages with coordinated acylic diagrams (DAG). Yuu likewise authored the accompanying definitions for herself: A change b1,b2,… ,bn fulfills a DAG G′ if for all edge u→v in G′, we should have bu<bv. A k-encoding is a DAG Gk on the arrangement of vertices 1,2,… ,n with the end goal that a stage b1,b2,… ,bn fulfills Gk if and provided that b is k-comparative. Since Yuu is free today, she needs to sort out the base number of…
Consider the wffs:φ1 ≡ p1 → (p2 → (p3 → p4))φ2 ≡ (p1 ∧ p2 ∧ p3) → p4(a) Technically speaking, neither φ1 nor φ2 is well-formed since neither is allowed by the formal syntaxof propositional logic. Correct them. Note, however, that we will freely make such trivial ’errors’ throughout this semester (as do most such courses).(b) Use truth tables (in the form defined in this course) to show that φ1 ↔ φ2.(c) After internalizing an intuitive understanding of this equality, propose an extension of it to n atoms.(d) State the number of rows in a truth table for proving the extension
Consider the wffs:φ1 ≡ p1 → (p2 → (p3 → p4))φ2 ≡ (p1 ∧ p2 ∧ p3) → p4(a) Technically speaking, neither φ1 nor φ2 is well-formed since neither is allowed by the formal syntaxof propositional logic. Correct them. Note, however, that we will freely make such trivial ’errors’throughout this semester (as do most such courses).(b) Use truth tables (in the form defined in this course) to show that φ1 ↔ φ2.(c) After internalizing an intuitive understanding of this equality, propose an extension of it to natoms.(d) State the number of rows in a truth table for proving the extension.
Justify your usage of a particular machine learning model and the problem it could solve. Two primary approaches exist for classifying objects: (A) relying on memory and (C) using a K-nearest neighbour algorithm.
Define a sequence c0, c1, c2, … of pictures recursively as follows:For all integers i ≥ 1 Initial Conditions, c0 = an upright equilateral triangle ?. Recurrence Relation, ci = in centre of each upright equilateral triangle in ci-1, draw an upside down equilateral triangle ? such that its corners touch the edges of the upright one. Draw the first 4 iterations, starting with c0. You may want to draw c3 large. Each should be a separate drawing.Get your work checked by an IA/TA/Instructor. Count the total # of triangles for each iteration in a).Note: Triangles can be of any orientation.Only count the individual triangles. Do not count a triangle which has triangles inside it. Determine T(0), the # of triangles in the 0th term. Determine the recurrence relation, T(n), that gives the # of triangles in the nth term, for n ≥ 1.
Suppose propositional sentences and knowledge-base here. We have a knowledge-base called KB. KBPrime is defined as an union of (1) KB and (2) the negation of a propositional predicate P. Answer true/false to the following questions. Note that "|=" is used to denote entailment, and "|-" is used to denote derivation through resolution. a) If KB |= P, then KB |- P. That is, if KB entails P, then KB derives (using resolution) P. b) If KB |- P, then KB |= P. c) If KBPrime |- [], then KBPrime is not satisfiable. d) If KBPrime is not satisfiable, then KBPrime |- [].