[理工] [離散] 邏輯

[TNC (code)]

92 雲科資工
If Archimedes was tall, then Euclid was short.
Euclid was not short unless Pythagoras was fat.
Pythagoras was fat only if he ate too much.
Pythagoras did not eat too much.
Therefore, Archimedes was not tall. Is the above logic inference valid?
解答
令 p Archimedes was tall
   q Euclid was short
   r Pythagoras was fat
   s Pythagoras ate too much
   則上述推論相當於
   1. p -> q
   2. (~q and ~r) or (q and r)
   3. r -> s
   4. ~s
   ~s 可導出~r(由 34) ~r又導出~q(由2)  ~q再得~p(由1)

請問:1.為什麼unless相當於 (~q and ~r) or (q and r)
     2.由4及3可推出 ~r(這邊沒問題)  而導出 ~r後為什麼會再得出 ~q

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 203.77.45.92
推 yyc1217:E不矮除非P胖 也就是E不矮，所以P不胖，除非P胖，則E也矮