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Let A be a set of formulas such that: a) Every finite subset of A is satisfiable and b) For every formula a, either a EA or (a) E 4. The truth assignment v is defined: (T if A E A F if A & A for each symbol of the statement A. Prove that for every formula , v (p) = V if and only if p E 4. v(A): =

Let A be a set of formulas such that: a) Every finite subset of A is satisfiable and b) For every formula a, either a EA or (a) E 4. The truth assignment v is defined: (T if A E A F if A & A for each symbol of the statement A. Prove that for every formula , v (p) = V if and only if p E 4. v(A): =

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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Mathematical logic Formula set properties. Let A be a set of formulas such that: a) Every finite subset of A is satisfiable and b) For every formula a, either a € 4 or (α) E 4. The truth assignment v is defined: (T if A E A if A & A for each symbol of the statement A. Prove that for every formula , v¯ (p) = V if and only if 4 E 4. Please be as clear as posible. Use definitions if necessary. Show and explain all the steps of the proof. Than you very much! v(A) = {F
Transcribed Image Text:Mathematical logic Formula set properties. Let A be a set of formulas such that: a) Every finite subset of A is satisfiable and b) For every formula a, either a € 4 or (α) E 4. The truth assignment v is defined: (T if A E A if A & A for each symbol of the statement A. Prove that for every formula , v¯ (p) = V if and only if 4 E 4. Please be as clear as posible. Use definitions if necessary. Show and explain all the steps of the proof. Than you very much! v(A) = {F
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