LSAT 7Sage Quantifiers (to share)

What are Quantifiers?

Words that indicate an ambiguous range of quantities (of qualified members belonging to a group)

What are the Quantifier words?

All, Overwhelming Majority, Most, Many, Some, Few, None

What does quantifier "All" mean?

100% (this is one of the only quantifiers that is not ambiguous, it means exactly what it says, All)

What is the Lower bound of "All"?

There is no Lower bound as "All" is not a range, it means all members of the group

What is the Upper bound of "All"?

There is no Upper bound as "All" is not a range, it means all members of the group

Diagram of "All"

What is "All" in "LAWgic"?

A-> B

All A are B

What is the negation for "All" (also in LAWgic)?

Original:

All A are B

A-> B

Negation:

Some A are not B

A <- S -> /B

What does quantifier "Overwhelming Majority" mean?

More than "Most"

What is the Lower bound of "Overwhelming Majority"?

More than "Most" (Most is more than 50%, OM is above that)

What is the Upper bound of "Overwhelming Majority"?

"All" (but implies a little below all)

Diagram of "Overwhelming Majority"

What does quantifier "Most" mean?

More than 50%

What is the Lower bound of "Most"?

More than Half (>50%)

What is the upper bound of "Most"?

"All" (but implies below all)

Diagram of "Most"

What is "Most" in "LAWgic"?

A -M-> B

One way arrow, can't flip groups around, the group after "Most" goes before the arrow and the other one goes after

Ex. Most Students in Mrs. Stoops's class can read.

Student -M-> Read

What is the negation for "Most" (also in LAWgic)?

Original:

Most A are B

A-m-> B

Negation:

It's not the case that Most A are B

/(A -m-> B)

What does quantifier "Many" mean?

A large number, large %

What is the Lower bound of "Many"?

Higher than "Some" (Some is 1 or more, so higher than 1, but very similar range)

What is the Upper bound of "Many"?

"All" (but implies below all)

Diagram of "Many"

What does quantifier "Some" mean?

At least 1

What is the lower bound of "Some"?

1

What is the upper bound of "Some"?

"All" (but strongly and almost certainly implies below all)

Diagram of "Some"

What is "Some" in "LAWgic"?

A <- S -> B

Two way arrows, each group can go to either side

Ex. Some Students in Mrs. Stoops's class can read.

Student <- S -> Read

Read <- S -> Student

(These mean the same thing)

What is the negation for "Some" (also in LAWgic)?

Original:

Some A are B

A <- S -> B

Negation:

No A are B

A-> /B

What does quantifier "Few" mean?

Not many, small %, Most are not

What is the lower bound of "Few"?

There is not a defined bound but assumption is at least 1

What is the upper bound of "Few"?

There is not a defined bound but assumption of less than half

Diagram of "Few"

What does "Not All" mean?

At least 1 exception to the rule/quantifying group

What does quantifier "None" mean?

Zero, 0% (this is one of the only quantifiers that is not ambiguous, it means exactly what it says, None)

What is the Lower bound of "None"?

There is no Lower bound as "None" is not a range, it means all members of the group

What is the Upper bound of "None"?

There is no Upper bound as "None" is not a range, it means all members of the group

Diagram of "None"

What is the sequence of inference with "Must be true"?

All -> Most -> Many -> Some -> Few

"All" implies what?

"All" ->____ ->____

"Most" and/or "Some"

All -> Most -> Some

"Most" Implies what?

Most -> ____

"Some"

Most -> Some

"Some" is most similar to and can be used almost interchangeably with what? ("Most" or "Many")

"Many"

Can "Some" imply "Most"?

No

Can "Some" imply "All"?

No

What is the negation of a conditional statement (also in Lawgic)?

Original:

If A then B

A -> B

Negation:

A can occur and B not occur

A and /B