Mathematical logicFormula set properties.Let A be a set of formulas such that:a) Every finite subset of A is satisfiable andb) For every formula a, either a € 4 or (α)E 4. The truth assignment v is defined:(T if A E Aif A & Afor 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 theproof. Than you very much!v(A) = {F

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Answered: Let A be a set of formulas such that:…

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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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): =