feifei91：if and only if A then B

jacky6ch

首先请问一个问题，if and only if A then B, 或者简单点only if A then B，为什么是B推出A呢？意思不是当且仅当A，则B吗？为什么是B推出A啊？

91. Leachate is a solution, frequently highly contaminated, that develops when water permeates a landifill’s site. If and only if the landfill’s capacity to hold liquids is exceeded does the leachate escape into the environment, generally in unpredictable queantities. A method must be found for disposing of leachate. Most landfill leachate is sent directly to sewage treatment plants, but not all sewage plants are capable of handling the highly contaminated water.

Which one of the following can be inferred from the passage?

(A) The ability to predict the volume of escaping landfill leachate would help solve the disposal problem.

(B) If any water permeates a landfill, leachate will escape into the environment.

(C) No sewage treatment plants are capable of handling leachate.

(D) Some landfill leachate is sent to sewage treatment plants that are incapable of handling it.

(E) If leachate does not escape from a landfill into the environment, then the landfill’s capacity to hold liquids has not been exceeded.

答案选E，给的解释是设If and only if the landfill’s capacity to hold liquids is exceeded为（A）， does the leachate escape into the environment为（B）。分析为：if and only if A then B(从B可以推出A)，则If not A then not B(非A推出非B，你否命题正确)。可是选项E不是说的是非B则非A吗？？！！请高人指点。

beichenxuans

以下是引用jacky6ch在2009/8/27 11:09:00的发言：

首先请问一个问题，if and only if A then B, 或者简单点only if A then B，为什么是B推出A呢？意思不是当且仅当A，则B吗？为什么是B推出A啊？

91. Leachate is a solution, frequently highly contaminated, that develops when water permeates a landifill’s site. If and only if the landfill’s capacity to hold liquids is exceeded does the leachate escape into the environment, generally in unpredictable queantities. A method must be found for disposing of leachate. Most landfill leachate is sent directly to sewage treatment plants, but not all sewage plants are capable of handling the highly contaminated water.

Which one of the following can be inferred from the passage?

(A) The ability to predict the volume of escaping landfill leachate would help solve the disposal problem.

(B) If any water permeates a landfill, leachate will escape into the environment.

(C) No sewage treatment plants are capable of handling leachate.

(D) Some landfill leachate is sent to sewage treatment plants that are incapable of handling it.

(E) If leachate does not escape from a landfill into the environment, then the landfill’s capacity to hold liquids has not been exceeded.

答案选E，给的解释是设If and only if the landfill’s capacity to hold liquids is exceeded为（A）， does the leachate escape into the environment为（B）。分析为：if and only if A then B(从B可以推出A)，则If not A then not B(非A推出非B，你否命题正确)。可是选项E不是说的是非B则非A吗？？！！请高人指点。

layer NN 曾经说过 only if    引出必要条件
 

                                     if    引出充分条件
 

具体请搜 充分必要条件指示词

[此贴子已经被作者于2009/8/27 12:41:13编辑过]

jacky6ch

谢谢，可是能不能帮我解释一下这道题啊？他的分析跟正确选项对不上号啊……

jacky6ch

哪位牛牛帮解决一下啊！！！

thmthm

同问！搜到另外一个讨论贴也没人回答！

如果按解释，是Only if A, then  B.

                所以，B推A。

取逆否，则是非A推非B。 那是没超过容水能力，就没escape。

答案说反了。

是不是因为这道题是if and only if ??所以可以两边推？？？

请牛人解答！！实在是不解！谢谢了！

thmthm

找到了  http://forum.chasedream.com/dispbbs.asp?boardid=24&replyid=298106&id=37650&page=1&skin=0&Star=2

jacky6ch

弱弱的问一句：比如我要在论坛里面搜一道讨论过的题我应该怎么搜啊？

thmthm

以下是引用jacky6ch在2009/9/4 17:06:00的发言：

弱弱的问一句：比如我要在论坛里面搜一道讨论过的题我应该怎么搜啊？

http://forum.chasedream.com/dispbbs.asp?boardID=24&ID=74827&page=1

overthere33

if and only if A then B 表示A是B的充分且必要条件

A <---> B 或者 B <---> A

only if A then B 表示A是B的必要条件 翻译过来就是只有A 那么B

所以是 B ---〉A

注意还有一种情况 if only A then B 这里only仅仅是强调 其实等于if A then B