SDCAR2010【逻辑入门】（十四）Formal Logic (2)

wyfhope

LZ在哪个学校上学呢，感觉楼主很牛啊

mia113

I made a silly mistake. thanks a lot``
From my perspective, for the question that needs to connect the gap: A-->B, GMAC prefer to make a trap that 非A cannot -->B, because many people will use this given information to infer that A -->B, while actually it is unjustifiable.

sdcar2010

I made a silly mistake. thanks a lot``
From my perspective, for the question that needs to connect the gap: A-->B, GMAC prefer to make a trap that 非A cannot -->B, because many people will use this given information to infer that A -->B, while actually it is unjustifiable.

-- by 会员 mia113 (2011/8/24 23:40:10)

Good thinking!

innerwarrior

Unless

The word unless can also create an if-then relationship. But it can be the most confusing and counterintuitive “logic” word. Consider this example:
Your CR score will not be high unless you study formal logic.

There are two ways to translate this statement into if-then clauses:
1) If your CR score is high, then you have studied formal logic.
2) If you did not study formal logic, then your CR score will not be high.

The second method is the foolproof way, which replaces unless with if not. The preferred way is the first method, which negate the clause before unless and cap it with if, and replace unless with then. Basically the clause after unless is the necessary condition which must happen for the negated form of the other clause. Back to the example we have here, “study formal logic” is a necessary step for one to get high score in CR. Without “studying formal logic”, one would not be able to score a high mark in CR. But “studying formal logic” alone might not be sufficient to help you score high in CR.

When the unless-clause comes at the beginning of the sentence, everything between the word unless and the comma is the unless-clause.


Either

The word either can also create an if-then relationship. Consider this example:
Either Peking University or Tshinghua University is on the list of my dream schools.

Given this rule, if PKU is not on my list, then THU is on my list because one of them must be. Further, the rule does not exclude the possibility that both schools are on my list. Therefore, the correct way to say the same thing using if-then clauses is:
If PKU is NOT on my list, then THU is.
Notice the word NOT is added to the if-clause, not the then-clause. Otherwise, we would make the mistaken assumption that both schools cannot be on the list together, which is not necessarily true—at least on the GMAT or LSAT.


Hidden if-then statements

Many if-then statements on the test are hidden because they do not use if or then. Instead, they use words like all, any, when, must and so on. Consider this example:
All Chinese students are diligent.
Translation: If you are a Chinese student, then you are diligent. (I truly hope so!!)

The trick here is that all means if.

There are also words that mean then. Here is another example:
Reading SDCAR’s posts on CR requires good understanding of English.
Translation: If you can read SDCAR’s posts on CR, then you have good understanding of English. (Pat yourself on the back, please!!)

Here are more words you can use to find hidden if-then statements:

If: All, always, any, each, every, in order to, invariably, no, none, things that, those who, to, when.

Then: Depends on, essential, must, necessary, needs, only, only if, only when, prerequisite, requires.

Unless (if not): Except, until, without.


No
When you see no at the beginning of a sentence, change no to if and negate the other clause, which is your then clause. Example:
No one who has a cold should go outside. (No X is Y.)
Translation: If you have a cold, then you should NOT go outside. (If X, then NOT Y.)


Most, some, and not all
Most means more than half. Most could be all.
Some means at least one. Some = Many. Some could be most, could be all.
Not all means some did not. Not all could be none.

SDCAR2010【逻辑入门】（十三）Formal Logic (1)

SDCAR2010【逻辑入门】（十五）More on Negation

-- by 会员 sdcar2010 (2011/7/20 11:51:18)

Dear SDCAR,

As the "NO" part, I have one question:
For example: No one who is good at basketball can play tennis well.
I knew it equals to "One who is good at basketball cannot play tennis well."
My question is : does the example also equals to "One who is not good at basketball can play tennis well"
if yes, it's not the 逆否命题. or Lawyer's suggestion is wrong? thx

My question is from Lawyer's one tip:
No mathematical proposition can be proventrue by observation. It follows that it is impossible to know any mathematicalproposition to be true.
The conclusion follows logically if whichone of the following is assumed?
(A) Only propositions that can be proventrue can be known to be true
(B) Observation alone cannot be used to provethe truth of any proposition.
(C) If a proposition can be proven true byobservation then it can be known to be true.
(D) Knowing a proposition to be true isimpossible only if it cannot be proved true by observation
(E) Knowing a proposition to be truerequires proving it true by observation
该题：推理：因为mathematical proposition NO PROVE BY OBSERVATION，所以mathematical propositionIMPOSSIBLE KNOW TO BE TRUE(概念跳跃为PROVE By observation，KNOW)。推理方向从NO PROVEBY OBSERVATION到 IMPOSSIBLEKNOW。（注意：这里没有充分必要关系，即不能将原文写成NO PROVE BY OBSERVQATION---〉IMPOSSIBLE KNOW。）

A：意思为proposition KNOWN TO BE TRUE--->ROPOSITION CAN BE PROVE。该选项很容易混。因为推理方向对：逆否命题从NO PROVE 到IMPOSSIBLE KNOW。且概念也很象，包含和被包含的概念（proposition包含mathematical proposition），概念比原文大在这类题中是允许的。但它错在没有说明PROVE的方式，原文有说明PROVE的方式为BY OBSERVATION。这也是和E选项的唯一区别。所以A选项加BYOBSERVATION便为答案。

B：没有KNOW的概念。错

C：CAN BE PROVE BY OBSERVATION---〉 KNOWN TO BE TRUE。逆否命题为IMPOSSIBLE KNOWN TO BE TRUE--->CANNOT BE PROVE BY OBSERVATION。和原文推理相反。错

D：IMPOSSIBLE KNOWN TO BE TRUE--->CANNOT BE PROVE BY OBSERVATION.和原文推理相反。错。

E：KNOWN TO BE TRUE--->CAN BE PROVE BY OBSERVATION（注意REQUIRE带必要条件）。逆否命题为：CANNOT BE PROVE BYOBSERVATION---〉IMPOSSIBLEKNOWN TO BE TRUE。和原文推理方向一致。正确答案。

注明：该题较特殊。除了两个推理相反的选项。还有一个概念相似的混淆项。

sdcar2010

Dear SDCAR,

As the "NO" part, I have one question:
For example: No one who is good at basketball can play tennis well.
I knew it equals to "One who is good at basketball cannot play tennis well."
My question is : does the example also equals to "One who is not good at basketball can play tennis well"

-- by 会员 innerwarrior

Correct: One who can play tennis well is not good at basketball.
Wrong: One who is not good at basketball can play tennis well.

Which part of lawyer's explanation you do not understand or have questions?

nobody910

Dear SDCAR,

I have some issue on your last point ---Most, some, and not all

You said,
Most could be all;
Some could be most, could be all.
Not all could be none.

Could you please illustrate through some examples? Thanks.

sdcar2010

Suppose we have 100 people, then

1) All = 100 people
2) Many = between 1 and 100 people (inclusive)
3) Some = between 1 and 100 people (inclusive, and yes, some = many in GMAT and LSAT)
4) Not all = between 0 and 99 people (inclusive)
5) Most = between 51 and 100 people (inclusive)

sh84682

CR好难啊……

hartmann

Thanks a lot `sdcar2010
But I'm confused why you classified about the one question related to the "no"
In an attempt to reduce the crime rate, the governor is getting tough on criminals and making prison conditions harsher.Part of this effort has been to deny inmates the access they formerly had to college-level courses.However, this action is clearly counter to the governor’s ultimate goal, since after being released form prison, inmates who had taken such courses committed far fewer crimes overall than other inmates.
Which of the following is an assumption on which the argument depends?

A.Not being able to take college-level courses while in prison is unlikely to deter anyone from a crime that he or she might otherwise have committed.
B.Former inmates are no more likely to commit crimes than are members of the general population.
C.The group of inmates who chose to take college-level courses were not already less likely than other inmates to commit crimes after being released.
D.Taking high school level courses in prison has less effect on an inmate’s subsequent behavior than taking college-level courses does.
E.The governor’s ultimate goal actually is to gain popularity by convincing people that something effective is being done about crime.

Correct answer is:C

However for the choice A:
Not being able to take college-level courses while in prison (X) is unlikely to deter anyone from a crime (Y) that he or she might otherwise have committed.
Not X is unlikely Y
-->If x, is Y
that means being able to take college-level courses while in prison  is likely to deter anyone from a crime -->This sentence is just the gap needed
I'm totally faint....please help me...thanks a lot``

-- by 会员 mia113 (2011/8/23 17:44:44)

This is a necessary assumption question.

Answer A: Not taking course in prison will not deter crime.
Logically, this is not the same as "Taking course in prison will deter crime."

Besides, if you negate this answer choice, you will get "Not taking course will deter crime.". It is simply the negation of the conclusion, "Not taking course will not deter crime.".

812966141

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