Quantifiers

Question 1

Q-S-M-A stands for….?

Answer 1

Quiet/QUANTIFIERS
Someone/SOME
May be/MOST
Asleep/ALL

Question 2

SOME means

Answer 2

At least ONE, possibly all

Question 3

True or False?

SOME statements are reversible

Answer 3

TRUE

Diagram as:

A–some–B
B–some–A

(NOT S–>N conditions, DO NOT
USE ARROWS WITH MOST OR SOME)

Question 4

MOST means

Answer 4

MORE than half, or 50.1%; a majority

Question 5

True or False?

MOST statements are not reversible

Answer 5

FALSE

When reversing, change MOST to SOME

A–most–B (ie: MOST carrots are vegetables)
B–some-A (ie; SOME vegetables are carrots)

(NOT S–>N conditions, DO NOT
USE ARROWS WITH MOST OR SOME)

Question 6

ALL mean

Answer 6

Every single one

Question 7

True or False?

ALL statements are Sufficient–>Necessary statements

Answer 7

True

Diagram as:

A –> B
not B –> not A

Use –> arrows, as it IS a Sufficient–>Necessary condition

Question 8

NOT ALL means

Answer 8

SOME- Not all, but at least one

“Not all A’s are B’s”

A–some–not B

Question 9

Rules for making valid deductions with quantifiers:

Answer 9

Rule #1: MUST have a S–>N staement

(Exception to Rule 1: Two (2) MOST statements with LEFT (Sufficient) side in common

Rule #2: MUST have Sufficient in common

When combining statements, with S–>N AND a Quantifier, the arrow must point AWAY from the “SOME” or “MOST”

P1: A–some–B
P2: B –> C

Rule 1? yes. B–>C
Rule 2? S in common? yes (P1 reveresd: B–some–A)

New P: A–some–B–> C

C: A–some–C