1- Given the following Boolean expressions for F and a don't care function D. F(h,k,m,n)= hk`m'n'+ hk`mn+ h`k'mn+ h'k'm'n'+ h`kmn+ hkmn D(h,k,m,n)= h'km`n'+ hkm`n'+ h'km`n+ hk`m`n+ h'k'm`n+ hkm`n i- Complete the truth table for F and D (Table.1) Table. 1 3 4 6. 9. 10 11 12 13 14 15 ---|-|-

Note that for this question, you can in addition use ``land” for the symbol ``lor" for the symbol V ` `Inot" for the symbol ¬ Given the following three sentences: A) Every mathematician is married to an engineer. B) A bachelor is not married to anyone. C) If George is a mathematician, then he is not a bachelor. a) Convert A,B,C into three FOL sentences, where Mn(x): x is a mathematician. Er(x): x is an engineer. Md(x,y): x is married to y. Br(x): x is a bachelor. george: George is a constant. b) Show that A does-not-entail C. (Hint: Consider defining an interpretation / such that / models A, but does-not-model C.) c) Show that {A,B} entails C. (Hint: For a given interpretation I, consider two difference cases, the case where Mn(george) is true, and the case Mn(george) is false. For both cases, argue that it is always that I models C). d) Convert A,B, Inot C into a set of clausal forms, number your clauses. (Note that C is negated here!) e) Derive the empty clause from the set of…