Show that the statement(Vx P(x)) V (Væ Q(x)) → Væ (P(x) V Q(x))is a tautology. Show that its converse is not a tautology by giving a counterexample.

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Answered: Show that the statement (V P(x)) V (Vx…

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 each of the following arguments using 1) Chain of Reasoning; and 2) Proof by Resolution. Vx [[F(x) - L(Juan,x)] Vx vy[ (E(x.y) V -D(x) - Fly) ] -3x [ A(x) A D(x)1 E(Maria, durian)A A(Maria) . LIJuan,durian) A. where F(x): x is food L(x.y): x likes to eat y E(x.y): x eats y D(x): x dies A(x): x is alive Vx[ (A(x,UP) A W(x,Lotto) - H(x)1 Vx vy[ (S(x) V L(x)) - A(x.y) ] Vx [ Lx) - W(x,Lotto) ] -S(Isko) A L(Isko) . H(Isko) where A(x.y): x is accepted at y (y is a university) W(x.y): x wins y B. poipnis x :(x)s L(x): x is lucky H(x): x is happy A challenge: For every statement in your chain of reasoning proof for parts A & B write down the equivalent in English. For example, the first premise in the argument in Part B translates to: Anyone who is accepted at UP and wins the Lotto is happy.
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Show that the statement (V P(x)) V (Vx Q(x)) → Vx (P(x) V Q(x)) is a tautology. Show that its converse is not a tautology by giving a counterexample.