• Lessons, Homework, & Extra Study
• Drilling, Timed Sections, & PTs
• Core Curriculum & Daily Live Classes

Intro to the course & study resources

• Be punctual - Try to arrive on time; class will start promptly.
• Stay on topic - Friendly banter is welcome, but let’s keep it to a minimum.
• Wait your turn - Raise your hand if you have a question. Don’t talk over people.
• Please be nice - Avoid using language that may be hurtful to your peers.
• Outside of class - Students are welcome to interact outside class. Remember that what happens outside class is outside the bounds of 7Sage moderation.

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Ground rules

Components of an LR question

(A)

(B)

(C)

(D)

(E)

Logical Reasoning Question Types

02.

Stimulus types

Welsh Corgis are known for their short legs, long bodies, and endearing personalities. Most people find this combination of features desirable in a pet dog.

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Set of Facts

Argument

A set of statements comprised of at least one premise and at least one conclusion.

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Premise

A statement designed to provide support to the conclusion.

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Conclusion

A statement designed to be supported by a premise.

Welsh Corgis are known for their short legs, long bodies, and endearing personalities. Most people find this combination of features desirable in a pet dog. Thus, most people would be happy owning a Welsh Corgi.

What is an argument?

P: Welsh Corgis have short legs, long bodies, and endearing personalities.

P: Most people find that combination of features desirable in a pet dog.

C: Most people would be happy owning a Welsh Corgi.

Order Doesn’t Matter

How to identify premises and conclusions

Author opinion

Why should I believe X? Because…Y.

Testing the logical flow

Why should I believe Y? Because…X.

or

• Tigers are members of endangered species. Thus, nobody should own tigers as pets.

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• Tigers are members of endangered species. Nobody should own a member of an endangered species as a pet. Thus, nobody should own tigers as pets.

Logical Validity and Assumptions

• Tigers are members of endangered species. Thus, nobody should own tigers as pets.

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• Tigers are members of endangered species. Nobody should own a member of an endangered species as a pet. Thus, nobody should own tigers as pets.

All invalid arguments make at least one assumption.

Assumption

Unstated or missing premise

Evaluating Logical Validity

• All apples are fruit.

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• If it’s raining, the sidewalk is wet.

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• In order to get on the plane, you need to have a ticket.

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• If you are a senior, you must report to the principal’s office.

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• Any officer who risked their life to save a civilian will be awarded a medal of bravery.

Conditional Reasoning - Part 1

What are examples of conditional statements?

Conditional relationship

A relationship between two conditions where the truth of one condition is sufficient to guarantee the truth of the other

Sufficient Conditions & Necessary Conditions

All apples are fruit.

All apples are fruit.

Sufficient Conditions & Necessary Conditions

Fruit

Sufficient Conditions & Necessary Conditions

Sidewalk wet

In order to get on the plane, you need to have a ticket.

Sufficient Conditions & Necessary Conditions

Have ticket

The conditional arrow

→

I’m holding an apple.

I’m holding a fruit.

Valid Inferences from a Conditional

Triggering the Sufficient Condition

apple → fruit

What is the

contrapositive?

For any conditional:

1. Switch the terms on each side of the conditional.

2. Negate both terms.

Valid Inferences from a Conditional

Triggering the Contrapositive (Denying the Necessary Condition)

apple → fruit

NOT fruit → NOT apple

/fruit → /apple

fruit → apple

The thing I’m holding is not a fruit.

The thing I’m holding is not an apple.

Valid Inferences from a Conditional

Triggering the Contrapositive (Denying the Necessary Condition)

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apple → fruit

[NOT fruit → NOT apple]

Invalid Inferences from a Conditional

“Triggering” the Necessary Condition

apple → fruit

I’m holding a fruit.

I’m holding an apple.

Invalid Inferences from a Conditional

Denying the Sufficient Condition

apple → fruit

The thing I’m holding is not an apple.

The thing I’m holding is not a fruit.

Summary: Valid and Invalid Inferences from a Conditional

• If a pizza has pineapples, it’s delicious.

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• A pizza is delicious if it has pineapples.

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• All pizzas with pineapples are delicious.

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• Deliciousness is a quality possessed by every pizza that has pineapples.

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• The only pizzas with pineapples are delicious.

Basic Conditional Indicators

• If [sufficient condition]
• When(ever) [sufficient condition]
• Where(ever) [sufficient condition]
• All [sufficient condition]
• Any [sufficient condition]
• Every [sufficient condition]
• Each [sufficient condition]
• The only [sufficient condition]

Group 1: Introduces a

Sufficient Condition

Pineapple on pizza → delicious

• Only people who are not seasick can be happy on a boat.
• One can be happy on a boat only if they are not seasick.
• People who are happy on boats are always devoid of seasickness.
• One must not be seasick to be happy on a boat.

Basic Conditional Indicators

• Only [necessary condition]
• Only if/when/where [necessary condition]
• Always [necessary condition]
• Must [necessary condition]

Group 2: Introduces a Necessary Condition

Happy on boat → NOT seasick

If you are a senior, you must report to the principal’s office.

Anyone who reports to the principal’s office will get detention.

Connecting Conditional Statements

senior → must report to principal’s office

must report to principal’s office → detention

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senior → must report to principal’s office → detention

detention → must report to principal’s office → senior

Quantifiers - Part 1

All of my friends are at the party.

Thus, most of my friends are at the party.

Thus, some of my friends are at the party.

Some of the classes are interesting.

Thus, most of the classes are interesting.

Thus, all of the classes are interesting.

Most of the babies are cute.

Thus, all of the babies are cute.

Thus, some of the babies are cute.

Summary: Valid and Invalid Inferences from a Conditional

LR Question Type – Must Be True (MBT)

Question Stem Examples:

• If all of the statement above are true, which of the following must be true?
• What can be properly inferred from the statements above?

Stimulus Features:

• Set of facts (no need to identify conclusions and premises).
• Often features conditional reasoning.

Process after IDing MBT question:

• Read stimulus carefully.
• Make connections between statements if they are warranted.
• Don’t make unwarranted connections.
• Eliminate answers that do not have to be true based on the stim.
• Pick the answer that must be true based on the stim.

Only people who are willing to compromise should undergo mediation to resolve their conflicts. Actual litigation should be pursued only when one is sure that one's position is correct. People whose conflicts are based on ideology are unwilling to compromise.

10. If the statements above are true, then which one of the following must be true?

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A. People who do not undergo mediation to resolve their conflicts should be sure that their positions are correct.

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B. People whose conflicts are not based on ideology should attempt to resolve their conflicts by means of litigation.

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C. People whose conflicts are based on ideology are not always sure that their positions are correct.

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D. People who are sure of the correctness of their positions are not people who should undergo mediation to resolve their conflicts.

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E. People whose conflicts are based on ideology are not people who should undergo mediation to resolve their conflicts.

A person with a type B lipid profile is at much greater risk of heart disease than a person with a type A lipid profile. In an experiment, both type A volunteers and type B volunteers were put on a low-fat diet. The cholesterol levels of the type B volunteers soon dropped substantially, although their lipid profiles were unchanged. The type A volunteers, however, showed no benefit from the diet, and 40 percent of them actually shifted to type B profiles.

20. If the information above is true, which one of the following must also be true?

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A. In the experiment, most of the volunteers had their risk of heart disease reduced at least marginally as a result of having been put on the diet.

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B. People with type B lipid profiles have higher cholesterol levels, on average, than do people with type A lipid profiles.

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C. Apart from adopting the low-fat diet, most of the volunteers did not substantially change any aspect of their lifestyle that would have affected their cholesterol levels or lipid profiles.

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D. The reduction in cholesterol levels in the volunteers is solely responsible for the change in their lipid profiles.

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E. For at least some of the volunteers in the experiment, the risk of heart disease increased after having been put on the low-fat diet.

Everyone in Biba's neighborhood is permitted to swim at Barton Pool at some time during each day that it is open. No children under the age of 6 are permitted to swim at Barton Pool between noon and 5 P.M. From 5 P.M. until closing, Barton Pool is reserved for adults only.

5. If all the sentences above are true, then which one of the following must be true?

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A. Few children under the age of 6 live in Biba's neighborhood.

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B. If Biba's next-door neighbor has a child under the age of 6, then Barton Pool is open before noon.

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C. If most children who swim in Barton Pool swim in the afternoon, then the pool is generally less crowded after 5 P.M.

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D. On days when Barton Pool is open, at least some children swim there in the afternoon.

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E. Any child swimming in Barton Pool before 5 P.M. must be breaking Barton Pool rules.

LR Question Type – Must Be True (MBT)

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Takeaways:

• Be careful about extreme language in the answer choices. All else equal, weaker answer are easier to prove based on the stimulus.
• Be on the lookout for conditional logic. Take the time visualize or diagram sufficient conditions and necessary conditions. (Eventually you won’t need to do this as much.)