Quantified Statements

Question 1

Most (Definition)

Answer 1

Indicate that more than 1/2 of the group have a certain property.
Most As are Bs
51% to 100%
Cannot reverse
Cannot take contrapositive
(Must be true, Parellel, Sufficient Questions)

Question 2

Negate “Most”

Answer 2

At least half… not
0-50%

Question 3

All

Answer 3

100%
Normal conditional statement
Cannot reverse
Contrapositive is always valid
(Must be true, Parellel, Sufficient Questions)

Question 4

Some (Definition)

Answer 4

At least 1 member of a group has certain property
Some As are Bs
Are reversible
Don’t always have valid contrapositive
(Must be True, Parellel, Sufficient Questions)

Question 5

Negate “Some”

Answer 5

None

Question 6

None

Answer 6

0

Question 7

Negate “None”

Answer 7

At least 1

Question 8

Negate “All”

Answer 8

0-99%
Not all…
Some…

Question 9

Diagram an “All” statement

Answer 9

A—>B
/B—>/A

Question 10

Diagram an “Most” statement

Answer 10

A-m->B

Question 11

Diagram an “Some” statement

Answer 11

A-s-B
B-s-A

Question 12

Combine
All + Some Statement

Answer 12

Shared term is the sufficient condition of the All statement, results in a “some” statement using the other two terms
A—>B
A-s-C
———
B-s-C

Question 13

Two Most Statements

Answer 13

Shared term is the sufficient condition of both “Most” statements; results in a “some” statement using the other two terms

A-m->B
A-m->C
———
B-s-C

Question 14

All + Most Statements

Answer 14

TWO valid ways:
1. Shared term is the sufficient condition of the “All” & “Most” statements; results in a “Some” statement using other two terms

A—>B
A-m->C
———-
B-s-C

2. Shared term is the necessary condition of the “Most” statements & the sufficient condition of the “All” statement; results in a “Most” statement using the other two terms

A-m->B
B—>C
———
A-m->C

Question 15

Quantified Statements that can never be validly combined

Answer 15

Most + Some
Some + Some