Question

Consider the following problem: Section II Con n a truth function f, find a statement S, only intolring the connecti e, ^,V and whose trva function is j. (a) Exhibit an algorithm that solves this problem. (b) Applied the exhibited algorithm to the truth function, 1 given by: TITIT (c) Suppose that the truth function f has n arguments represented by the variables i Consider the first algorithm studied in class to solve the problem of item (a). Let 01,92,.... In be the component statements associated to the variables Pro are assigned the jth combination of values for the variables · ….z" in the definition of statement s, defined in the second step of this algoritham is only true if a . ii. Use the previous item to conclude that two diferent s,'s cannot be true for the saae combi nation of truth values fr qi,虹…-An. ili. Prove that this algorithm properly works. 2. Translate the following sentence into a formula: If one arbitrary instant of time is after a second arbitrary Instant of time, then there is an instant of time after the second and before the first. (a) Ex (b) Exhibit one atomic fornmula present in this formula. (c) Deter hibit one term of this formula. quantißers that oceur in this mine the scope of each of the this formula contain a free variable? Justilfy (e) Does this formula constitute a statement? Justify. proof for it. 3. I the following argument is valid, provide is virtwous. f eroticism is virtuous, then either duty is not the of pleasure. But the sopreme duty is not the pursuit t then eroticism is virtuoss If hedonism is correc is not correct. the highest irtue or of pleasure Therefore, either duty is not The End

Answer 1

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