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 V-C. Deductive Reasoning (Must Be True questions)

Deductive reasoning questions are the last topic we cover because they are an entirely different species from the rest of the LSAT critical reasoning questions.

Note: these questions are rare on the LSAT. You do not have to memorize the rules, just learn how to apply them.

Deductive vs. Inductive Reasoning

These questions force you to follow highly specific logical rules. Most critical reasoning questions use soft and fuzzy inductive reasoning (with observations, lots of unstated assumptions, etc). Deductive reasoning is what a computer would do: hard logic following rules. You often use deductive reasoning in the legal field.

1. You were on the neighbor's property
2. It is against trespassing laws to be on the neighbor's property.
3. You are therefore guilty of trespassing.

Isaac Inductive says: I've noticed that every time I kick soccer ball up, it comes back down, so I guess this next time when I kick it up, it will come back down again.

Dennis Deductive says: You are merely applying Newton's law of gravity. Everything that goes up must come down. If you kick the ball up, it must come down.

Types of Deductive Reasoning

Which of the following could be answered using pure deductive reasoning:

1. Did the growth of the population of Connecticut slow last year?
3. Are Connecticut legal residents also residents of the United States?
4. Does Connecticut has the highest per capita income of any state in the United States?

This is a bit of a trick question. Which ones of the above are deductive?

1. It seems obvious to look at population data, but what about migrant workers, etc.. who may not be documented. With heavy assumptions you are making an inductive guess.

2. This relies on surveying popular opinion about who appreciates access to the ocean and that data is fraught with assumptions.

3. In 1789, Connecticut became the first signatory to the U.S. constitution and all Connecticut legal residents of the United States. This is pure deductive reasoning by just applying legal text.

4. The income of Connecticut residents is difficult to measure and this is an observational task, not a deductive one. So this is inductive reasoning.

Rule #1: If A, then B
If I press the power button, then the computer will turn off.

1. Valid Inference: If not B, then not A
If the computer is on, then I didn't press the power button.
(this logic rule is called the Contrapositive)

2. Invalid Inference: If B, then A
The computer is off; therefore I pressed the power button.
(There are other ways it could have shut off.)

3. Invalid Inference: If not A, then not B
If I did not press the power button, then the computer is not off.
(There are other ways it could have shut off, this is called Denying the Antecedent.)

Example: Denying the Antecedent
If rains, then the grass is wet.
It isn't raining, then the grass must be dry
(There could have a sprinkler system).

Rule #2: If A, then B, If B, then C
If A, then B: If I press the power button, the computer will turn off.
If B, then C: If the computer is off, then the web site will shut down.

1. Valid Inference: If A, then C
If I press the power button, then the web site will shut down.

2. Valid Inference: If not C, then not A
If the web site is not shut down, then I did not press the power button.

3. Invalid Inference: If C, then A
If website is shut down, then I must have pressed the power button.
(There are other ways it could have shut off).

Rule #3: All A are B

1. Valid Inference: All non-B's are non-A's.
A test that is not adaptive is not a LSAT.

2. Valid Inference: No non-B is an A.
No test that is not adaptive is a LSAT.

3. Invalid Inference: No non-A's are B's.

4. Invalid Inference: All B are A.
All adaptive tests are LSAT tests.

Rule #4: All A are B, All B are C.
All A are B: All LSATs are adaptive
All B are C: All adaptive tests are computerized tests.

1. Valid Inference: All A are C
All LSAT tests are computerized.

2. Valid Inference: No non-C is an A
No non-computerized test is a LSAT.

3. Invalid Inference: No non-A is a C
No non-LSAT test is computerized.

4. Invalid Inference: All C are A
All computerized tests are LSAT tests.

Rule #5: Some A are B.
Some programs are part-time programs

1. Valid Inference: Some B are A
Some part-time programs are MBA programs.

2. Invalid Inference: Some A are not B
Some MBA programs are not part-time.

3. Invalid Inference: Some B are not A
Some part-time programs are not MBA programs.

Rule #6: Some A are B and Some B are C
Some A are B: Some MBA programs are part-time programs
Some B are C: Some part-time programs are poetry degrees.

1. Valid Inference: Some B are A
Some part-time programs are MBA programs.

2. Valid Inference: Some C are B
Some poetry degrees are part-time programs.

3. Invalid Inference: Some A are C
Some MBA programs are poetry degrees.

4. Invalid Inference: Some C are A
Some poetry degrees are MBA programs.

Why are C and D invalid? Although A and C share B, they don't necessarily share the part of B that links both of them.

Rule #7: Some A are B and All B are C.
Some A are B: Some MBA programs are accounting programs
All B are C: All accounting programs are math intensive programs

1. Valid Inference: Some B are A
Some accounting programs are MBA programs.

2. Valid Inference: Some A are C
Some MBA programs are math intensive programs.

3. Valid Inference: Some C are A
Some math intensive programs are MBA programs.

4. Invalid Inference: All C are A
All math intensive programs are MBA programs.

5. Invalid Inference: All C are B
All MBA programs are math intensive programs.

Rule #8: Either A or B, but not both
Either a dog or a cat

1. Valid Inference: If A, then not B
If a dog, then not a cat.

2. Valid Inference: If B, then not A
If a cat, then not a dog.

3. Valid Inference: If not B, then A
If a not a cat, then a dog.

4. Valid Inference: If not A, then B
If a not a dog, then a cat.

There are two main types of Deductive Reasoning (Must Be True) Questions:

1. Make a deduction: extend the premises to make a direct logical conclusion?

• If the statements above are true, which of the following must also be true?
• Which of the following may be correctly inferred?
• Which of the following inferences (inference means the same thing as "must be true" on the test) is best supported by the statement made above?
(Conclusions differ from inferences in that conclusions are the result of premises and inferences must be true if the premises are true.)

2. What's the missing premise? Here you find out what premise would be necessary to make the argument logically valid.

• The passage's conclusion is only true if which of the following statements is also true?
• Which of the following, if introduced into the argument as a premise, makes the argument logically correct?
 Most critical reasoning questions are about what may or may not be true based on assumptions. Examples are: which of the following is the best, the most or the least likely to satisfy the question. Deductive questions will never use those indicators. They are written in terms of certainty: must be true, required, necessary, etc...

How to tackle Deductive Reasoning (Must Be True Questions):

1. Read the passage and look for the argument. Note that Must Be True questions may not be an argument. They may just be a series of facts. Nevertheless, try to find the argument.

2. Must Be True questions should always be tackled using POE (process of elimination). Go through every answer choice systematically and check if it is ALWAYS true. If you can find a situation where it is not true, eliminate it. Gradually eliminate answer choices until you have one left.

Example

Every store on Main Street in Summitville has an awning and all of these awnings are either green or red.
If the statement above is true, which one of the following must also be true?

I. Some awnings in Summitville are green.
II. If a store in Summitville does not have an awning, then it is not on Main Street .
III. If a store in Summitville has a red awning, then it is on Main Street .

1. I only
2. II only
3. I and II only
4. I and III only
5. I, II, and III

Explanation: Note that this question is not an argument per se because it requires deductive reasoning.

Statement I may not be true. The question states that all of the awnings on Main Street are either green or red, but this does not preclude the possibility that all of the awnings on Main Street are red.

Statement III may not be true either. The question states that every store on Main Street has either a red awning or a green awning, but this does not preclude the possibility that a store on some other street has a red awning.

Statement II must be true. If every store on Main Street has an awning, then a store without an awning cannot be on Main Street . The correct answer is B.

Example

The mathematical constant ‘e’ ( the base of the natural logarithm) is transcendental and therefore irrational.  In 1882, the mathematician Johann Heinrich Lambert proved that the number ‘pi’ is irrational.  'Pi' must therefore be transcendental.

Which of the following statements, if true, most weakens the conclusion drawn above about the number pi

1. The exact value of transcendental numbers cannot be given.
2. The number √2 is irrational but not transcendental.
3. The mathematician Fernard von Lindermann used the fact that e is transcendental to prove that pi is transcendental.
4. The number √3 is transcendental but not irrational.
5. It is extremely difficult to prove that a number is transcendental.

This question asks you to weaken the conclusion, which states that pi must be transcendental.  The key phrase here is “must be”. We know ‘e’ to be transcendental and therefore irrational, but all we’re told about pi is that it is irrational, so the conclusion that pi must therefore be irrational is unfounded.  Pi might be irrational (and in fact is), but the information in the passage can’t logically lead us to that conclusion.  A statement weakening the conclusion will show that pi is not necessarily transcendental.  Choices A, C and E are irrelevant. Choice B states that a number can be irrational and not transcendental. This shows that pi is not necessarily transcendental.  Choice D gives us the reverse of what we want since it tells us that a number can be transcendental and not irrational.  We already know that pi is irrational, so this doesn’t weaken the conclusion.  Choice B does, and is the best answer.

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