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Theory and Problems in Discrete Mathematics (29)

Theory and Problems in Discrete Mathematics (29) - I...

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I- V.'.RVy(-x = y - -y = x) Vx(Fx -+ Gx), -Fa t 3x -x = a 3x3yLxy I- 3x3y(Lxy & -x = y) t VxVy ((Fxy & x = y) - Fyx) VI Formalize each and every of the following arguments, using the interpretation given under. Then construct a refutation tree to examine whether or not the type of the argument is legitimate or invalid. Image Interpretation Names P r (10) 'Fa' is a wff, via rule 1; and considering 'h = a' is a wff via the guideline for identification, '-6 = a' is a wff, via rule 2. Accordingly '(Fa* -b = a)' is a wff, by means of rule 3, whence two functions of rule four it follows that 'VxVy(Fx - -y = x)' is a wff. I11 (5) real (10) False (15) False (20) proper IV (5) This argument is invalid. Any model in which 'I;' designates a nonempty class whose members do not include the interpretation of 'a' makes the premise '3xFx' proper and the conclusion 'Fa' false. PREDICATE logic 167
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If M is a model wherein the premise is correct, then there exists at the least one a-variant M' of M wherein '3y(Ma & new york)' is correct (with the aid of situation (5)). For that
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