Quantifier Math & Diagraming Flashcards
All + All =
Some
- Sufficient condition of BOTH terms are shared
Most + Most =
some
- sufficient condition (left) of oth terms are shared.
Most + Some =
nothing.
can never combine
All + Some
Some
- sufficient condition of “ALL” matches either one of the “some” terms
Some + Some =
Nothing.
Can never combine.
Inverse or Converse
OG: A->B
/A/ -> /B/
Inverse
Inverse or Converse
OG: A -> B
B -> A
Converse
How do you diagram
“Not all”
Change to some
Negate the concept that comes in the second half of the statement.
How do you diagram
“most”
group “most” applies to –m–> characteristic we are saying most of them have.
- no cp
- no inverse / converse
All + Most =
Some: sufficient of the “all” matches sufficient of the “most” = some
Most: - sufficient of the “all” matches necessary of the “most” = most
What is a good rule of thumb to follow when trying to determine to diagram or not?
General Rule:
Whenever the question uses:
- unless - until
-without - except
All introduce a negated sufficient.
(another way to think about it, change to “if not”)
When do you use the “no torpedo” & when do you NOT use the “no torpedo” ?
use: Anytime you have a “no quantity” statement.
i.e. None of this is that.
* Zero quantity of this thing has this characteristic *
NOT USE: Anytime there is another conditional indicator in the same sentence. Use the other conditional indicator.
How do you deny a conditional claim?
Affirm the sufficient & deny the necessary
Ex: A-> B
Negation : A-> /B/
How do you diagram a “no torpedo”?
- what follows the “no” is your sufficient [DO NOT TOUCH IT] & the “no” will negate the necessary.
essentially, “ No” introduces the sufficient and negates the necessary.
What does “some” negated become?
none
If and Any together in the same sentence
- “If” overpowers the “any”.
sufficient is what follows the if.
When diagraming conditional statements; what rule of thimb do you follow when diagrmaing grammatical statements?
Suff: what are we getting facts about
Necess: What’s true about the subject.
What is the quantifier rule of thumb to follow?
If you have two quantity statements AND they share a condition AND that shared condition is the sufficient of an “ALL” statement, then you can combine those statements together.
If NOT, you cannot combine them together with the ecpetion of two “most” statements that share the same sufficient.
