Quantifiers - Basics Flashcards
DEFINE:
All
100%
VISUALIZE:
All A are B.
All A are B means that the A group is entirely within the B group. There can be many Bs that are not As, but all As are Bs.
Note that we DON’T know exactly how big the B circle is. So it’s possible that most Bs are A or even that All Bs are A. But these don’t have to be true.
Common synonyms for “ALL” on the LSAT?
Every
Each
Any
Anyone
Everyone
Are statements quantified by “ALL” conditional relationships?
YES.
All A are B
is equivalent to
If A —> then B
/B —> /A
DEFINE:
Most
Over 50%
More than half
VISUALIZE:
Most A are B.
Over half of the A circle is within the B circle.
Note that it’s possible that All A are B, it’s just this doesnt have to be true. Similarly, it’s possible that Most B are A; it’s not something that must be true, however. This is why a MOST statement is not reversible. Most A are B does not imply that Most B are A.
Common synonyms for MOST on the LSAT?
Majority
Usually
Likely*
Probably
*A is likely to be Z = Most A are Z.
But “likely” is different from “more likely”. Saying that Y is more likely than T does not mean that Y happens most of the time.
DIAGRAM:
Most K are W.
K —most—> W
This means over half of the group K is W.
There is NO contrapositive of a MOST statement.
MOST statements aren’t reversible (although you can conclude that Some W are K).
DEFINE:
Some
At least one
VISUALIZE:
Some A are B.
At least part of A and B overlap with each other.
Common synonyms for SOME on the LSAT?
Many*
A few*
Often*
*These words don’t mean literally the same thing as “at least one”. However, for the purpose of making inferences from quantified statements on the LSAT, you can treat them as SOME statements.
DIAGRAM:
Some E are Q.
E some Q
Q some E
Some statements are reversible, which is why you shouldn’t use an arrow to diagram them. If at least one E is a Q, then it must be true that at least one Q is an E.
There is NO contrapositive of a SOME statement.
TRUE OR FALSE:
We should usually diagram a quantified statement when we see one in logical reasoning.
FALSE
Diagramming quantified statements is useful only when the problem is about drawing inferences from more than one quantified statement. The vast majority of “most” and “some” on the LSAT are just individual statements that are not meant to combine with other statements, and it would be a waste of time to diagram these.
Read the stimulus first to get a sense of what the problem is trying to test. If it’s about combining quantified statements, then a diagram can be useful.
VALID OR INVALID?
Premise: All H are D.
Conclusion: Some H are D.
VALID
If 100% of H are D, then it must be true that at least one H is a D.
If you thought thought this was invalid, then you might have thought that “Some H are D” implies that “Some H are NOT D”. That’s wrong; on the LSAT, “some” does not imply that “some are not”. Some means anywhere from just 1 all the way up to 100%.
VALID OR INVALID?
Premise: Most N are J.
Conclusion: Some J are N.
VALID
If over half of N are J, then there must be at least one N that is a J. In other words, there must be some N that are J. And SOME statements are always reversible. If some N are J, that means at least one J is an N.
