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