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

> 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.
p O q = (p v q)^ ~(p ^ q).
(pvq)v (р лr) and (p V q)лг
~(p A q) and ~p v ~q
Easily add text in PDF
Add
Question 06
• Use truth tables to verify the following logical equivalences. Include a few
words of explanation with your answers.
p →q = ~p V q
а.
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) → p
a.
b. -р — (р — q)
р — (руq)
c.
Question 08
• Determine whether the statement forms are logically equivalent using Logic
Algebra.
> P→ q = ¬q → -p
(PA Q) V (PA ~Q) V (~P^ ~Q) = PV ~Q
• ~(~p ^ q) ^ (p v q) = p
Bonus

equivalences hold.
1. Commutative laws: p Aq = q ap
pv q = q vp
2. 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 =p
pv c = p
5. Negation laws: p v ~p = t
pA ~p = c
6. Double negative law: ~(~p) = p
7. Idempotent laws: p ^p =p
pv p = p
8. Universal bound laws: p v t = t
pAC=C
9. De Morgan's laws: ~(p ^ q) = ~p V ~q
- (p v q) = ~p A ~q
10. Absorption laws: p v (p A q) =p
pA (p v q) = p
11. Negations of t and c: ~t = c
-C = t
12. Removing implication: p → q = -p v q
-(p → q) = p A ng
Table 1
Question 05
• 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.
p O q = (p v q)^ ~(p ^ q).
(p v q) v (p Ar) and (p v q)ar
~(p ^ q) and ~p v ~q
Question 06
• Use truth tables to verify the following logical equivalences. Include a few
words of explanation with your answers.
p →q = ~p V q
a.
b. p →q = (p^ ~q) →( r ^ ~r)
~(р —q) %3D р л ~д.
C.
d. p
q = (p- q) A (q → p)
Question 07
> Determine whether the statement forms are Tautology using Logic Algebra.
а. (рлд) —р
b. -р — (р — q)
p - (p v g)
c.

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