必要条件和充分条件

Necessary Conditions

必要条件

If we say that "x is a necessary condition for y," we mean that if we don't have x, then we won't have y. Or put differently, without x, you won't have y. To say that x is a necessary condition for y does not mean that x guarantees y.

如果我们说“X是Y的必要条件，”我们的意思是：如果我们没有X，那么我们就不会有Y。换言之，没有X，你就不会有Y。说X是Y的必要条件，不意味着X保证Y。

Some examples will help here.

下面的一些例子会帮助你理解：

Having gasoline in my car (I have a gasoline engine) is a necessary condition for my car to start. Without gasoline (x) my car (y) will not start. Of course, having gasoline in the car does not guarantee that my car will start. There are many other conditions needed for my car to start.

我车里有汽油，是我开车的必要条件。没有汽油（X），我的汽车（Y）就不会开得动。当然，我的汽车里有汽油，不担保我的汽车会开动。对开动我的汽车而言，需要有许多其他条件。

Having oxygen in the earth's atmosphere is a necessary condition for human life. Certainly, having oxygen will not guarantee human life. There are many other conditions needed for human life other than oxygen in the atmosphere.

大气里有氧气是人类生命的必要条件。肯定地说，有氧气不担保人类生命。对人类生命而言，除了大气里有氧气之外，还有许多其他条件。

Being 18 years of age is a necessary condition for being able to buy cigarettes legally in North Carolina. Of course, being 18 does not guarantee that a person will buy cigarettes. There are many other conditions that lead to a person buying cigarettes than being 18 years of age.

年满18岁是在北卡州合法地买烟的必要条件。当然，年满18岁不担保一个人会买烟。导致一个人买烟的，除了18岁之外，还有许多其他条件。

Sufficient Conditions

充分条件

If we say that "x is a sufficient condition for y," then we mean that if we have x, we know that y must follow. In other words, x guarantees y.

如果我们说“X是Y的充分条件，”那么我们的意思是：如果我们有X，那么我们知道Y就紧随其后。换言之，X担保Y。

Consider the following examples.

考虑下面的例子：

Earning a total of 950 points (95%) in this Critical Thinking class is a sufficient condition for earning a final grade of A. If you have 950 points for the course, then it must follow that you will have a final grade of A.

在“严密思维”这门课上，一共得到950分，是最后成绩得A等的充分条件。如果你在本课得到950分，那么必随其后的是你将得到最后成绩A等。

Pouring a gallon of freezing water on my sleeping daughter is sufficient to wake her up. If I pour the gallon of freezing water on her then its guaranteed that she will wake up.

把一加仑冰水倒在我睡觉的女儿头上，足以让她醒来。如果我们把一加仑冰水倒在她头上，那就担保她会醒来。

Rain pouring from the sky is a sufficient condition for the ground to be wet.

天下雨是地湿的充分条件。

Please note that in none of these example is the sufficient condition also a necessary condition.

注意，这些例子中，没有一个例子的充分条件也是必要条件（换言之，那个充分条件也可能是其他的条件，而不见得是提到那个）。

For example, it is not necessary to earn 950 points to earn an A in this course. You can earn 920 points to earn an A. (We cannot say that if you do not have 950 points then you can't have an A.)

例如，在这门课上，一共得到950分，对最后成绩得A等而言，是必要的。你可以得920分，以得到A。（我们不能说：如果你得不到950分，那么你就不可能得A等。）

It is not necessary to pour a gallon of freezing water on my daughter to wake her up. (A wrecking ball against the wall will do it as well.)

把一加仑冰水倒在我睡觉的女儿头上，对让她醒来而言，是必要的。（强拆队的推土机推翻一堵墙，也会把她弄醒。）

Similiarly, it is not necessary for rain to be pouring from the sky for the ground to be wet. The sprinkler could be on as well.

与此相似，对地湿而言，天下雨不见得是必要的。

Test your knowledge of necessary and sufficient conditions by trying the following:

看下面的例子，是必要条件还是充分条件：

Is sunlight a necessary or sufficient condition for the roses to bloom?

阳光是玫瑰开花的必要条件还是充分条件？

Is earning a final grade of C a necessary or sufficient condition for passing the course?

就通过这门课而言，最终成绩C是必要条件还是充分条件？

Is being a male a necessary or sufficient condition for being a father?

对当父亲而言，身为男子是必要条件还是充分条件？

Is having the flu virus in your blood a necessary or sufficient condition for being sick?

对生病而言，你血液里有流感病毒是必要条件还是充分条件？

Is attending class regularly and punctually a necessary or sufficient condition for being successful in class?

按时按点上课，对学好这门课而言，是必要条件还是充分条件？

Is being 20 years old a necessary or sufficient condition for being a college student?

就成为大学生而言，年满20岁是必要条件还是充分条件？

答案：click here 。