SDCAR2010【逻辑入门】（十三）Formal Logic (1)

sdcar2010

If-Then Statements

Example: If you run a red light in Beijing, then youwill get a ticket for 300 RMB.

To diagram this statement, let’s shorten the original statement byrepresenting each clause with one letter:

If R, then T.

R stands for “you run a red light in Beijing”

T stands for “you will get a ticket for 300 RMB”

From the original statement, we can infer that:

If not T, then not R.

In other words, if someone has never gotten a ticket (not T), then thatperson must not have run a red light in Beijing (not R). Basically, the newstatement switches the clauses and then negates both variables. This newif-then statement or inference is called a “contrapositive.” If the originalstatement is true, then contrapositive must also be true. Because both theoriginal and the contrapositive statements are logically equivalent, thecontrapositive is just another way of stating the original statement.

CommonMistakes

The problem is that many people apply only one of the steps above. Theyonly switch or they only negate. Neither of these two operations on theoriginal statement will produce an equivalent of the original one.

Original: If you run a red light in Beijing, then youwill get a ticket for 300 RMB. (If R, then T.)

Mistake one: If you got a ticket for 300 RMB, then you rana red light in Beijing. (If T, then R.)

The problem is you might be fined because you were speeding, not becauseyou were running a red light. So we cannot conclude that “you ran a red light”simply because “you got a ticket.”

Mistake two: If you did not run a red light in Beijing, then youwill not get a ticket for 300 RMB.

Again, this statement is obviously wrong since you could get a ticketfor speeding.

Negating And and Or

When you negate and, it becomes or.And when you negate or, it becomes and.

Example:

Statement: If you eat a poison,you will get sick and call your mom.

If P, then S and M

Contrapositive:

If you did not get sick or did not call your mom, you did not eat a poison.

If not S or not M, then not P.

It is important to use or herebecause using and wouldgo too far.

Only If

Like the words if and then,the phrase onlyif can also create andif-then relationship. But it can be confusing. Even though onlyif ends with if it does not introduce the if-clause.In fact, onlyif introduce the then-clause;whatever comes immediately afteronly if is then then-clause. The rest of thestatement is the if-clause.

Example:

Ming attends the meeting only if Hua attends.

Translation: If Ming attends the meeting, then Hua attends.

Only if you wear a shirt will you enter this restaurant.

Translation: If you enter this restaurant, then you were a shirt.

If andOnly If

The phrase if and only if actually introduces two rules. Consider thisexample:

The Shanghai Shark will win the tournament if, and only if, it has YaoMing as its center.

In this sentence, both if and onlyif introduce the lastclause—“it has Yao Ming as its center.” Yet if introducesif-clause and only if introducesthen-clause.

Translation: “If Shanghai Shark has Yao Ming as its center, then it willwin the tournament” and “If the Shanghai Shark won the tournament, then it hadYao Ming as its center.”

SDCAR2010【逻辑入门】（十二）Principles

SDCAR2010【逻辑入门】（十四）Formal Logic (2)

梦季

感谢分享！               

梦季

顶楼主！               

sa0314

Mark一下！               

VincentFSJ

这么好的东西居然没有人顶！

Jacklizk

牛主，可否看下我的理解是否正确：
原文凝练：if abolish-》then improve
正确选项D： if improve->then Not abolish
如果是增强的话:if Not improve, then not abolish
所以是削弱，这样理解正确吗？
同是CR问题学生，有些时候真是抓不到点上；

echogmj

thx for sharing ~~~~

zhangyanlele

解释的好清楚，终于搞懂了他们的区别！

醒醒Shine

以前对only if一直有误解！谢谢楼主！终于明白only if引导的是必要条件啊，if引导的才是充分条件！

virgmat

sdcar2010 发表于 2011-9-18 20:59
D就是: If pharmaceutical companies can afford the research that goes into the development of new dru ...

觉得这句话的没转换准确，应该是〜

(D) Pharmaceutical companies canafford the research that goes into the development of new drugs only if patentsallow them to earn high profits.
= if pharmaceutical companies can afford the research that goes into the development of new drugs, then patents HAVE allowed them to earn high profit.

请指教〜