P, > Determine whether the statement forms are logically equivalent. In eachcase, construct a truth table and include a sentence justifying your answer.Your sentence should show that you understand the meaning of logicalequivalence.p O q = (p v q)^ ~(p ^ q).(pvq)v (р лr) and (p V q)лг~(p A q) and ~p v ~qEasily add text in PDFAddQuestion 06• Use truth tables to verify the following logical equivalences. Include a fewwords of explanation with your answers.p →q = ~p V qа.b. p →q = (p^ ~q) →(r ^ ~r)c. ~(p →q) = p ^ ~q.d. pg3 (р — q)л (q — р)Question 07> Determine whether the statement forms are Tautology using Logic Algebra.(p A q) → pa.b. -р — (р — q)р — (руq)c.Question 08• Determine whether the statement forms are logically equivalent using LogicAlgebra.> P→ q = ¬q → -p(PA Q) V (PA ~Q) V (~P^ ~Q) = PV ~Q• ~(~p ^ q) ^ (p v q) = pBonus equivalences hold.1. Commutative laws: p Aq = q appv q = q vp2. Associative laws: (p a q) Ar =p^ (qAr)(p v q) vr = p v (q v r)3. Distributive laws: p ^ (q v r) = (p ^ q) v (p ar)p v (q ar) = (p v q) ^ (p v r )4. Identity laws: p At =ppv c = p5. Negation laws: p v ~p = tpA ~p = c6. Double negative law: ~(~p) = p7. Idempotent laws: p ^p =ppv p = p8. Universal bound laws: p v t = tpAC=C9. De Morgan's laws: ~(p ^ q) = ~p V ~q- (p v q) = ~p A ~q10. Absorption laws: p v (p A q) =ppA (p v q) = p11. Negations of t and c: ~t = c-C = t12. Removing implication: p → q = -p v q-(p → q) = p A ngTable 1Question 05• Determine whether the statement forms are logically equivalent. In eachcase, construct a truth table and include a sentence justifying your answer.Your sentence should show that you understand the meaning of logicalequivalence.p O q = (p v q)^ ~(p ^ q).(p v q) v (p Ar) and (p v q)ar~(p ^ q) and ~p v ~qQuestion 06• Use truth tables to verify the following logical equivalences. Include a fewwords of explanation with your answers.p →q = ~p V qa.b. p →q = (p^ ~q) →( r ^ ~r)~(р —q) %3D р л ~д.C.d. pq = (p- q) A (q → p)Question 07> Determine whether the statement forms are Tautology using Logic Algebra.а. (рлд) —рb. -р — (р — q)p - (p v g)c.

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Determine whether the statement forms are logically equivalent. In each case, construct a truth table and include a sentence justifying your answer. Your sentence should show that you understand the meaning of logical equivalence. pOq = (p v q)A ~(p^ q). (p v q) v (p A r) and (p v q) ^ r ~(p A q) and ~p v ~q

Determine whether the statement forms are logically equivalent. In each case, construct a truth table and include a sentence justifying your answer. Your sentence should show that you understand the meaning of logical equivalence. pOq = (p v q)A ~(p^ q). (p v q) v (p A r) and (p v q) ^ r ~(p A q) and ~p v ~q

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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Question 1: In graph theory, a graph X is a "complement" of a graph F if which of the following is true? Select one: a. If X is isomorph to F, then X is a complement of F. b. If X has half of the vertices of F (or if F has half of the vertices of X) then X is a complement of F. c. If X has the same vertex set as F, and as its edges ONLY all possible edges NOT contained in F, then X is a complement of F. d. If X is NOT isomorph to F, then X is a complement of F. Question 2: Which statement is NOT true about Merge Sort Algorithm: Select one: a. Merge Sort time complexity for worst case scenarios is: O(n log n) b. Merge Sort is a quadratic sorting algorithm c. Merge Sort key disadvantage is space overhead as compared to Bubble Sort, Selection Sort and Insertion Sort. d. Merge Sort adopts recursive approach
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