3. (Laws of the Algebra of Propositions: Distributive Laws). (i) Construct the truth table of the proposition PV (q^r), and then (ii) the truth table of the proposition (pVq) ^ (pVr). Here and below (in Problems 4, 5), all your truth tables must reflect the process of building a compound proposition under consideration from propositional variables (your solution(s) will be downgraded, otherwise). Say, the truth table for the compound proposition in (i) must be as follows: p|qr|qAr pV (q^r) TTT TT F *** ⠀⠀⠀ ⠀ FFF (iii) Compare the truth tables, and make a conclusion on the equivalence of the propositions, thereby proving that pv (q^r) = (pVg) ^ (p Vr) (if your truth tables are not identical, redo the problem). To present the answers to the problem, please include in your document both truth tables you've created in (i,ii), followed by the conclusion you've made in (iii).
3. (Laws of the Algebra of Propositions: Distributive Laws). (i) Construct the truth table of the proposition PV (q^r), and then (ii) the truth table of the proposition (pVq) ^ (pVr). Here and below (in Problems 4, 5), all your truth tables must reflect the process of building a compound proposition under consideration from propositional variables (your solution(s) will be downgraded, otherwise). Say, the truth table for the compound proposition in (i) must be as follows: p|qr|qAr pV (q^r) TTT TT F *** ⠀⠀⠀ ⠀ FFF (iii) Compare the truth tables, and make a conclusion on the equivalence of the propositions, thereby proving that pv (q^r) = (pVg) ^ (p Vr) (if your truth tables are not identical, redo the problem). To present the answers to the problem, please include in your document both truth tables you've created in (i,ii), followed by the conclusion you've made in (iii).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. (Laws of the Algebra of Propositions: Distributive Laws). (i) Construct the truth table of the proposition
PV (q^r),
and then (ii) the truth table of the proposition
(pVq) ^ (pVr).
Here and below (in Problems 4, 5), all your truth tables must reflect the process of building a compound proposition under
consideration from propositional variables (your solution(s) will be downgraded, otherwise). Say, the truth table for the compound
proposition in (i) must be as follows:
p|qr|q^r pV (q^r)
TTT
TT F
⠀⠀⠀ ⠀
FFF
(iii) Compare the truth tables, and make a conclusion on the equivalence of the propositions, thereby proving that
pv (q^r) = (pVg) ^ (p Vr)
(if your truth tables are not identical, redo the problem).
To present the answers to the problem, please include in your document both truth tables you've created in (i,ii), followed by the
conclusion you've made in (iii).
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