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Some and Most Relationships

Existential Quantifiers Overview

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Relationship to Universal Quantifiers

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Existential Quantifiers Brief

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"Some" Statements Meaning

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"Some" Statements Translation

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"Most" Statements Meaning

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"Most" Statements Translation

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"Few" Statements Meaning and Translation

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Advanced: All Implies Most Implies Some

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Advanced: Negate Some Statements

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Advanced: Negate All Statements

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Deny the Relationship

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Quiz - Negation 1 w/ Answers

Quiz Instructions: 1. Translate all English statements into Lawgic. 2. Negate each statement in Lawgic. 3. Translate each statement back into English.

Question 1

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Tap to restore original All X-Wings have hyperdrives.

Answer

Some X-Wings don’t have hyperdrives. (X ←sβ†’ /H)

A thing can be an X-wing and not have hyperdrives. (X and /H)

Question 2

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Tap to restore original Some alphabets are not phonetic.

Answer

All alphabets are phonetic. (A β†’ P)

Question 3

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Tap to restore original No pilots are blind.

Answer

Some pilots are blind. (P ←sβ†’ B)

One can be a pilot and blind. (P and B)

Question 4

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Tap to restore original Some mice are fat.

Answer

All mice are not fat. (M β†’ /F)

No mice are fat.

Question 5

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Tap to restore original Everyone enjoys the movies.

Answer

Some people do not enjoy the movies. (P ←sβ†’ /M)

One can be a person and not enjoy the movies. (P and /M)

Any English translation of the above answers would be correct.

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Quiz - Negation 2 w/ Answers

Quiz Instructions: 1. Translate all English statements into Lawgic. 2. Negate each statement in Lawgic. 3. Translate each statement back into English.

Question 1

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Tap to restore original All non-water breathing mammals have limbs.

Answer

Some mammals don’t have limbs. (M ←sβ†’ /L)

One can be a mammal and not have limbs. (M and /L)

Question 2

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Tap to restore original No one can eat a hamburger without drinking beer.

Answer

Some people eat hamburgers without drinking beer. (H ←sβ†’ /B)

One can eat a hamburger and not drink beer. (H and /B)

Question 3

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Tap to restore original If more than three inches of snow accumulate, then classes will be canceled.

Answer

Three inches of snow accumulating is not sufficient to cancel class. /(3 β†’ C)

We could get three or more inches of snow accumulating and still have class. (3+ and /C)

Question 4

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Tap to restore original Some graduate level philosophy courses are available to undergraduates.

Answer

No graduate level philosophy courses are available to undergraduates. (G β†’ /U)

Question 5

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Tap to restore original If the record sells well, then you will be famous.

Answer

The record could sell well and you could still be not famous. (W and /F)

Some world exists where the record sells well and you are not famous. (W ←sβ†’ /F)

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Quiz - Negation 3 w/ Answers

Quiz Instructions: Negate each statement.

Question 1

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Tap to restore original Most people like ice cream.

Answer

It's not the case that most people like ice cream. not(P ‑mβ†’ I)

The proportion of people who like ice cream ranges from none to half.

Question 2

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Tap to restore original Some islands are more tropical than others.

Answer

All islands are equally tropical.

No island is more tropical than another.

Question 3

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Tap to restore original Most types of pasta are made from wheat.

Answer

Zero to exactly half of the types of pasta are made from wheat.

Question 4

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Tap to restore original Small animals can move more rapidly than large animals can.

Answer

Either large animals move more rapidly than small animals OR they (referencing large and small animals) move equally rapidly.

Question 5

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Tap to restore original Chess is the most appropriate analogy to reporting on political campaigns.

Answer

Either something else is more appropriate analogy for reporting on political campaigns than chess is OR something else ties with chess as being the most appropriate analogy for reporting on political campaigns.

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Quiz - Negation 4 w/ Answers

Quiz Instructions: Negate each statement.

Question 1

Tap to restore original The amount of energy needed to move uphill is no greater for large animals than it is for small animals.

Answer

It’s not the case that the amount of energy needed to move uphill is not greater for large animals than it is for small animals.

The amount of energy needed to move uphill is greater for large animals than it is for small animals.

Question 2

Tap to restore original Every doctor in this hospital is qualified to work on combating the city's zombie epidemic.

Answer

Some doctors in this hospital are not qualified to work on combating the city’s zombie epidemic. (D some /Q)

One can be a doctor in this hospital and not qualified to work on combating the city’s zombie epidemic. (D and /Q)

Question 3

Tap to restore original There is little variation in the ratio of energy output to body weight among animals.

Answer

It’s not the case that there is little variation in the ratio of energy output to body weight among animals.

There is anywhere from a moderate amount to a great amount of variation in the ratio of energy output to body weight among animals, or no variation at all.

Question 4

Tap to restore original Drug-related crime is not as serious a problem for the city as the mayor claims it is.

Answer

It’s not the case that drug-related crime is not as serious of a problem for the city as the mayor claims it is.

Drug-related crime is just as serious of a problem for the city as the mayor claims it is, or it is more serious.

Question 5

Tap to restore original You are always on my mind.

Answer

It’s not the case that you are always on my mind.

You are sometimes or never on my mind.

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Valid Argument Form (4 of 9)

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Valid Argument Form 4 - Review

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Valid Argument Form (5 of 9)

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Valid Argument Form 5 - Review

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Valid Argument Form (6 of 9)

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Valid Argument Form 6 - Review

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Valid Argument Form (7 of 9)

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Valid Argument Form 7 - Review

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Valid Argument Form (8 of 9)

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Valid Argument Form (9 of 9)

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Advanced Valid Forms

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Advanced Valid Forms Review

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