a) Prove the one point rule - 3-version: (3x)(x = t ^ A) = A[x = t] if x is not free in t. b) Prove the dual result 6 on p.176. Prove (3x) AVBC = (3x) ACV (3x) BC. (Hint: Translate first to Standard notation) c) Prove using the auxiliary variable metatheorem: + (3x)(A → B) → (Vx)A → (3x)B
a) Prove the one point rule - 3-version: (3x)(x = t ^ A) = A[x = t] if x is not free in t. b) Prove the dual result 6 on p.176. Prove (3x) AVBC = (3x) ACV (3x) BC. (Hint: Translate first to Standard notation) c) Prove using the auxiliary variable metatheorem: + (3x)(A → B) → (Vx)A → (3x)B
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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![a) Prove the one point rule - 3-version: (3x)(x = t ^ A) = A[x := t] if x is not free in t.
b) Prove the dual result 6 on p.176. Prove (3x) AvBC = (3x) ÂС V (3x) BC. (Hint: Translate first to Standard
notation)
c) Prove using the auxiliary variable metatheorem: + (3x) (A → B) → (Vx)A → (3x)B](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c803f28-d355-4a7f-8b24-1cdd50e60256%2F5a97c41b-252a-4f0a-9464-65854f80d130%2Ftuutldi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Prove the one point rule - 3-version: (3x)(x = t ^ A) = A[x := t] if x is not free in t.
b) Prove the dual result 6 on p.176. Prove (3x) AvBC = (3x) ÂС V (3x) BC. (Hint: Translate first to Standard
notation)
c) Prove using the auxiliary variable metatheorem: + (3x) (A → B) → (Vx)A → (3x)B
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