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Prove that the following arguments are invalid. (1) 1. (Gх)(Ах - Вх) 2. (3x)(Bx · Cx) 1:. (3x)(Ax · Cx) (2) 1. (х)(Ах Вx) 2. (3x) ~ Ax /.:. (3x) ~ Bx (3) 1. (Jx)(Ax · ~ Bx) 2. (3x)(Ax · ~ Cx) 3. (Вх)(~ Вх Dx) 1.. (Ex)[Ax · (~ Bx · Dx)] (4) 1. (x)(Fx Gx) 2. (x)(~ Fx Ɔ Ex) 1.. (x)(~ Gx Ɔ ~ Ex) (5) 1. (3x)(Px· ~ Qx) 2. (x)(Rx Ɔ Px) 1.. (3x)(Rx ·~ Qx)

Prove that the following arguments are invalid. (1) 1. (Gх)(Ах - Вх) 2. (3x)(Bx · Cx) 1:. (3x)(Ax · Cx) (2) 1. (х)(Ах Вx) 2. (3x) ~ Ax /.:. (3x) ~ Bx (3) 1. (Jx)(Ax · ~ Bx) 2. (3x)(Ax · ~ Cx) 3. (Вх)(~ Вх Dx) 1.. (Ex)[Ax · (~ Bx · Dx)] (4) 1. (x)(Fx Gx) 2. (x)(~ Fx Ɔ Ex) 1.. (x)(~ Gx Ɔ ~ Ex) (5) 1. (3x)(Px· ~ Qx) 2. (x)(Rx Ɔ Px) 1.. (3x)(Rx ·~ Qx)

Advanced Engineering Mathematics
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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Prove that the following arguments are invalid using the method of interpretation. Only answer questions 1, 3 and 5.

Prove that the following arguments are invalid. (1) 1. (Gх)(Ах - Вх) 2. (3x)(Bx · Cx) 1:. (3x)(Ax · Cx) (2) 1. (х)(Ах Вx) 2. (3x) ~ Ax /.:. (3x) ~ Bx (3) 1. (Jx)(Ax · ~ Bx) 2. (3x)(Ax · ~ Cx) 3. (Вх)(~ Вх Dx) 1.. (Ex)[Ax · (~ Bx · Dx)] (4) 1. (x)(Fx Gx) 2. (x)(~ Fx Ɔ Ex) 1.. (x)(~ Gx Ɔ ~ Ex) (5) 1. (3x)(Px· ~ Qx) 2. (x)(Rx Ɔ Px) 1.. (3x)(Rx ·~ Qx)
Transcribed Image Text:Prove that the following arguments are invalid. (1) 1. (Gх)(Ах - Вх) 2. (3x)(Bx · Cx) 1:. (3x)(Ax · Cx) (2) 1. (х)(Ах Вx) 2. (3x) ~ Ax /.:. (3x) ~ Bx (3) 1. (Jx)(Ax · ~ Bx) 2. (3x)(Ax · ~ Cx) 3. (Вх)(~ Вх Dx) 1.. (Ex)[Ax · (~ Bx · Dx)] (4) 1. (x)(Fx Gx) 2. (x)(~ Fx Ɔ Ex) 1.. (x)(~ Gx Ɔ ~ Ex) (5) 1. (3x)(Px· ~ Qx) 2. (x)(Rx Ɔ Px) 1.. (3x)(Rx ·~ Qx)
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