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某年级要从1班、2班、3班、4班、5班中选出一名才子主持元旦晚会,每班最多一人,也可能没有,这些人满足如下条件,请确定最终选择哪些班级的学生:(1)如果1班有人选中,则2班有人选中。(2)若5班有人选上则1班与2班均有人选上。(3)5班与4班必有一班有被选中。(4)3班与4班同时有人选上或同时没人选上。

某年级要从1班、2班、3班、4班、5班中选出一名才子主持元旦晚会,每班最多一人,也可能没有,这些人满足如下条件,请确定最终选择哪些班级的学生:(1)如果1班有人选中,则2班有人选中。(2)若5班有人选上则1班与2班均有人选上。(3)5班与4班必有一班有被选中。(4)3班与4班同时有人选上或同时没人选上。

发布时间:2025-03-22 17:11:24
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答案:解:用One表示1班选了人,Two表示2班选了人,Three表示3班选了人,Four表示4班选了人,Five表示5班选了人。则这4个条件依次为One→Two,Five→(One∧Two),Four∨Five,Three↔Four满足这4个条件,即这4个条件的值均为真即为1,所以其合取为1(One→Two) ∧(Five→(One∧Two)) ∧(Four∨Five) ∧(Three↔Four)=1,将以上合取范式转换为主析取范式,因此双条件应转换为析取式的合取式原式=(¬One∨Two) ∧(¬Five∨(One∧Two)) ∧(Four∨Five) ∧((¬Three∨Four)∧ (Three∨¬Four))=[(¬One∨Two) ∧(¬Five∨(One∧Two))] ∧(Four∨Five) ∧(¬Three∨Four)∧ (Three∨¬Four)=[(¬One∧¬Five)∨(¬One∧(One∧Two)∨(Two∧¬Five)∨(Two∧(One∧Two)]∧(Four∨Five) ∧(¬Three∨Four)∧ (Three∨¬Four)={[(¬One∧¬Five)∨(Two∧¬Five)∨(Two∧One)]∧(Four∨Five)}∧(¬Three∨Four)∧ (Three∨¬Four)={[(¬One∧¬Five∧Four) ∨( Two∧¬Five∧Four) ∨(Two∧One∧Four) ∨(Two∧One∧Five)]∧(¬Three∨Four)}∧ (Three∨¬Four)={(¬One∧¬Five∧Four∧¬Three) ∨(¬One∧¬Five∧Four) ∨(Two∧¬Five∧Four ∧¬Three) ∨(Two∧¬Five∧Four) ∨(Two∧One∧Four ∧¬Three) ∨(Two∧One∧Four) ∨(Two∧One∧Five ∧¬Three) ∨(Two∧One∧Five ∧Four)} ∧ (Three∨¬Four)=(¬One∧¬Five∧Four∧ Three) ∨( Two∧¬Five∧Four ∧ Three) ∨(Two∧One∧Four∧ Three) ∨(Two∧One∧Five ∧¬Three ∧ ¬Four) ∨(Two∧One∧Five ∧Four ∧ Three)= (¬One∧ Three ∧Four ∧¬Five) ∨( Two ∧ Three ∧Four ∧¬Five) ∨(One∧Two∧ Three ∧ Four) ∨(One∧Two∧¬Three∧ ¬Four∧ Five) ∨(One∧Two∧ Three ∧Four ∧ Five)(1)如果1班有人选中,则2班有人选中。(2)若5班有人选上则1班与2班均有人选上。(3)5班与4班必有一班有被选中。(4)3班与4班同时有人选上或同时没人选上。按照某位帅哥的质疑,经仔细思考,应该将其转换为主析取范式,所以最终结果为:= (¬One∧1∧ Three ∧Four ∧¬Five) ∨(1∧ Two ∧ Three ∧Four ∧¬Five) ∨(One∧Two∧ Three ∧ Four∧1) ∨(One∧Two∧¬Three∧ ¬Four∧ Five) ∨(One∧Two∧ Three ∧Four ∧ Five)= (¬One∧¬Two∧ Three ∧Four ∧¬Five) ∨(¬One∧Two∧ Three ∧Four ∧¬Five) ∨(¬One ∧ Two ∧ Three ∧Four ∧¬Five) ∨(One∧ Two ∧ Three ∧Four ∧¬Five) ∨(One∧Two∧ Three ∧ Four∧¬Five) ∨(One∧Two∧ Three ∧ Four∧Five) ∨(One∧Two∧¬Three∧ ¬Four∧ Five) ∨(One∧Two∧ Three ∧Four ∧ Five)=(¬One∧¬Two∧ Three ∧Four ∧¬Five) ∨(¬One∧Two∧ Three ∧Four ∧¬Five) ∨(One∧ Two ∧ Three ∧Four ∧¬Five) ∨(One∧Two∧ Three ∧ Four∧Five) ∨(One∧Two∧¬Three∧ ¬Four∧ Five)(1)如果1班有人选中,则2班有人选中。(2)若5班有人选上则1班与2班均有人选上。(3)5班与4班必有一班有被选中。(4)3班与4班同时有人选上或同时没人选上。
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