(Solved) : 7 12 Points Consider Following Argument Express Argument Bellow Using Propositional Variab Q44027352 . . .
7) (12 points) Consider the following argument and express the argument bellow, using propositional variables f, b and l. Is this argument valid? If so, prove its validity or if not, state why it is not valid. • Fry and Bender are not both innocent. • If Fry is not lying, Bender must be innocent. • Therefore, if Fry is innocent, then he is lying • Let f be the proposition “Fry is innocent” • Let b be the proposition “Bender is innocent” • Let l be the proposition “Fry is lying”. Hint: When False? Statement VxVy P(x, y) VyVxP(x, y) Vx3y P(x, y) When True? P(x, y) is true for every pair x, y. There is a pair x, y for which P(x, y) is false. For every x there is a y for which P(x, y) is true. There is an x such that P(x, y) is false for every y. 3r Vy P(x, y) There is an x for which P(x, y) is true for every y. For every x there is a y for which P(x, y) is false. P(x, y) is false for every pair x, y. 3x3y P(x, y) 3y3x P(x, y) There is a pair x, y for which P(x, y) is true. Statements involving nested quantifiers can be negated by successively applying the rules for negating statements involving a single quantifier. Show transcribed image text 7) (12 points) Consider the following argument and express the argument bellow, using propositional variables f, b and l. Is this argument valid? If so, prove its validity or if not, state why it is not valid. • Fry and Bender are not both innocent. • If Fry is not lying, Bender must be innocent. • Therefore, if Fry is innocent, then he is lying • Let f be the proposition “Fry is innocent” • Let b be the proposition “Bender is innocent” • Let l be the proposition “Fry is lying”.
Hint: When False? Statement VxVy P(x, y) VyVxP(x, y) Vx3y P(x, y) When True? P(x, y) is true for every pair x, y. There is a pair x, y for which P(x, y) is false. For every x there is a y for which P(x, y) is true. There is an x such that P(x, y) is false for every y. 3r Vy P(x, y) There is an x for which P(x, y) is true for every y. For every x there is a y for which P(x, y) is false. P(x, y) is false for every pair x, y. 3x3y P(x, y) 3y3x P(x, y) There is a pair x, y for which P(x, y) is true. Statements involving nested quantifiers can be negated by successively applying the rules for negating statements involving a single quantifier.
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Answer to 7) (12 points) Consider the following argument and express the argument bellow, using propositional variables f, b and l…
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