Use the change of quantifier rule together with the eighteen rules of inference to derive the conclusions of the following symbolized argument. Do not use either conditional proof or indirect proof. AB X(3x) (x) 3CQMPDist123UIMTDNUGEIHSDSTrans ImplPREMISE(x)BxDV =PREMISE(3x)~Ax V (3x)~BxPREMISEEGIIIIdCDEquivCONCLUSION~(x) Ax=th( ) { } []AddTaut ACPSimp ConjExpDMCPComAIPAssocIP

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A B X (3x) (x) 3 CQ MP Dist 1 2 3 UI MT DN UG EI HS DS Trans Impl PREMISE (x)Bx DV = PREMISE (3x)~Ax V (3x)~Bx PREMISE EG III Id CD Equiv CONCLUSION ~(x) Ax = th Simp Exp ( ) Conj Taut Add ACP DM CP [ ] Com AIP Assoc IP

A B X (3x) (x) 3 CQ MP Dist 1 2 3 UI MT DN UG EI HS DS Trans Impl PREMISE (x)Bx DV = PREMISE (3x)~Ax V (3x)~Bx PREMISE EG III Id CD Equiv CONCLUSION ~(x) Ax = th Simp Exp ( ) Conj Taut Add ACP DM CP [ ] Com AIP Assoc IP

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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Question

Use the change of quantifier rule together with the eighteen rules of inference to derive the conclusions of the following symbolized argument. Do not use either conditional proof or indirect proof.

A
B X
(3x) (x) 3
CQ
MP
Dist
1
2
3
UI
MT
DN
UG
EI
HS
DS
Trans Impl
PREMISE
(x)Bx
DV =
PREMISE
(3x)~Ax V (3x)~Bx
PREMISE
EG
III
Id
CD
Equiv
CONCLUSION
~(x) Ax
=
th
( ) { } []
Add
Taut ACP
Simp Conj
Exp
DM
CP
Com
AIP
Assoc
IP

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