Hi All,
I need some help understanding the notation used in the "10 Real LSATs Grouped by Question Type" by MLSAT. Here are the problems I'm having:
What does the tilde indicate?
How do I combine some/most statements using conditional diagramming?
I thought one of the "juicier" diagramming questions was PT43, S2, Q22. If someone could explain how the notations were arrived at (as per the solutions), I would greatly appreciate it. I wrote the question and solution down below:
All parrots can learn to speak a few words and phrases. Not all parrots have equally pleasant dispositions, though some of those native to Australia can be counted on for a sweet temper. Almost any parrot, however, will show tremendous affection for an owner who raised the bird from a chick by hand-feeding it.
Here is how it was diagrammed in the solutions:
P --> LS
P <-some-> ~PD
P <-some-> ST
P + HF-most --> SA
Many thanks!!
LSAT Forum
3 postsPage 1 of 1
-
- shaorahman
-
Thanks Received: 0
-
Vinny Gambini
- Posts: 5
- Joined: April 25th, 2015
-
- ohthatpatrick
-
Thanks Received: 3808
-
Atticus Finch
- Posts: 4661
- Joined: April 01st, 2011
- This post thanked 2 times.
Re: Advanced Conditional Diagramming
Great questions.
The tilde just means "not".
Sally --> ~John
"If Sally is in, then John is not".
========
I would personally never diagram a some / most statement. Conditional logic is reserved for CERTAINTY. Some and most don't provide certainty other than "at least one" in the case of SOME and "more than half" in the case of MOST.
That said, other companies and other teachers sometimes represent SOME and MOST with arrows in order to think about quantity inferences.
Quantity inferences are a major headache to students but a minor sideshow on the test. You frequently go an entire test without seeing one.
There are really three quantity inferences that are worth knowing, and I almost don't even wanna mention the third one (because it's so rare).
MOST COMMON
Combine an ALL / NONE idea with some other fact about the SUFFICIENT (left side) idea.
In the parrot example, we know that
IF you're a parrot, THEN you can learn to speak a few phrases.
Parrot -> Learn Speak
The idea with any conditional statement is that AS SOON AS YOU KNOW the left side idea applies, you're guaranteed of the right side idea as well.
So as soon as we find any other idea about Parrots, we can add/replace the idea of "learn to speak a few phrases".
NEW IDEA: not all parrots have equally pleasant dispositions
TRANSLATION: some parrots are more or less pleasant than others.
POSSIBLE INFERENCE: some [things that can learn to speak a few phrases] are more or less pleasant than other [things that can learn to speak a few phrases].
Does that make sense?
"Not all" is actually a tricky construction. You should memorize how to translate it correctly into "Some".
"Not all NFL players are female" is a true statement (despite the fact that it sounds like it's implying that many, if not most, NFL players ARE female).
'Not all' just means "less than 100%", so 0% is still less than 100%.
Not all A's are B's = Some A's are ~B's (not B's)
NEW IDEA: Some native Australian parrots have a sweet temper
POSSIBLE INFERENCE Some [things that can learn to speak a few phrases] are native to Australia. Some [things that can learn to speak a few phrases] have a sweet temper.
We're still just replacing PARROTS with that guaranteed idea we were given.
NEW IDEA: Most parrots that were hand-fed as a baby will show affection for owner.
POSSIBLE INFERENCE: Some [things that can learn to speak a few phrases] will show affection for owner if hand-fed as a baby.
In more symbolic terms:
All A are B
Some A are C
-----------------
Some B are C
Since 'Some' statements are reversible, people who diagram them do so with a double sided arrow.
"Some cats are smelly" = "at least one cat is smelly" and "at least one smelly thing is a cat"
Most statements are not reversible.
"Most US Senators are male" is not the same as "most males are US Senators".
So people who diagram Most do so with an arrow starting from the MOST group. If you ever wanted to go backwards, you would just read SOME. If I know that "MOST hand-fed parrots show affection" I can say that "SOME things that show affection are hand-fed parrots".
NEXT MOST COMMON QUANTITY INFERENCE
Most A's are B's
Most A's are C's
-------------------
Some B's are C's
When you have to majority facts about the SAME GROUP, then you can infer that there has to be at least one member in the group that has both qualities of the majority.
If I say Most senators are rich and Most senators are men, then there must be at least one rich man.
RARE QUANTITY INFERENCE
Most A's are B's.
All B's are C's.
What do you think we could infer from that?
Most Senators are rich.
All rich people have savings accounts.
Most Senators have savings accounts.
Notice that this is the only time we inferred a MOST overlap. That's very rare. Almost all quantity inferences you'll ever make are going to prove AT LEAST ONE (some / not all).
This would NOT work if I reversed the order.
All A's are B's.
Most B's are C's.
All Senators are rich.
Most rich people flaunt their wealth.
Does that mean that all / most / some Senators flaunt their wealth?
Nope. If there are 50,000 rich people in the world, then at least 25,001 of them flaunt their wealth.
But the 100 rich Senators discussed could easily be among the 24,999 rich people who don't flaunt their wealth.
Let me know if you're confused by any of this.
The tilde just means "not".
Sally --> ~John
"If Sally is in, then John is not".
========
I would personally never diagram a some / most statement. Conditional logic is reserved for CERTAINTY. Some and most don't provide certainty other than "at least one" in the case of SOME and "more than half" in the case of MOST.
That said, other companies and other teachers sometimes represent SOME and MOST with arrows in order to think about quantity inferences.
Quantity inferences are a major headache to students but a minor sideshow on the test. You frequently go an entire test without seeing one.
There are really three quantity inferences that are worth knowing, and I almost don't even wanna mention the third one (because it's so rare).
MOST COMMON
Combine an ALL / NONE idea with some other fact about the SUFFICIENT (left side) idea.
In the parrot example, we know that
IF you're a parrot, THEN you can learn to speak a few phrases.
Parrot -> Learn Speak
The idea with any conditional statement is that AS SOON AS YOU KNOW the left side idea applies, you're guaranteed of the right side idea as well.
So as soon as we find any other idea about Parrots, we can add/replace the idea of "learn to speak a few phrases".
NEW IDEA: not all parrots have equally pleasant dispositions
TRANSLATION: some parrots are more or less pleasant than others.
POSSIBLE INFERENCE: some [things that can learn to speak a few phrases] are more or less pleasant than other [things that can learn to speak a few phrases].
Does that make sense?
"Not all" is actually a tricky construction. You should memorize how to translate it correctly into "Some".
"Not all NFL players are female" is a true statement (despite the fact that it sounds like it's implying that many, if not most, NFL players ARE female).
'Not all' just means "less than 100%", so 0% is still less than 100%.
Not all A's are B's = Some A's are ~B's (not B's)
NEW IDEA: Some native Australian parrots have a sweet temper
POSSIBLE INFERENCE Some [things that can learn to speak a few phrases] are native to Australia. Some [things that can learn to speak a few phrases] have a sweet temper.
We're still just replacing PARROTS with that guaranteed idea we were given.
NEW IDEA: Most parrots that were hand-fed as a baby will show affection for owner.
POSSIBLE INFERENCE: Some [things that can learn to speak a few phrases] will show affection for owner if hand-fed as a baby.
In more symbolic terms:
All A are B
Some A are C
-----------------
Some B are C
Since 'Some' statements are reversible, people who diagram them do so with a double sided arrow.
"Some cats are smelly" = "at least one cat is smelly" and "at least one smelly thing is a cat"
Most statements are not reversible.
"Most US Senators are male" is not the same as "most males are US Senators".
So people who diagram Most do so with an arrow starting from the MOST group. If you ever wanted to go backwards, you would just read SOME. If I know that "MOST hand-fed parrots show affection" I can say that "SOME things that show affection are hand-fed parrots".
NEXT MOST COMMON QUANTITY INFERENCE
Most A's are B's
Most A's are C's
-------------------
Some B's are C's
When you have to majority facts about the SAME GROUP, then you can infer that there has to be at least one member in the group that has both qualities of the majority.
If I say Most senators are rich and Most senators are men, then there must be at least one rich man.
RARE QUANTITY INFERENCE
Most A's are B's.
All B's are C's.
What do you think we could infer from that?
Most Senators are rich.
All rich people have savings accounts.
Most Senators have savings accounts.
Notice that this is the only time we inferred a MOST overlap. That's very rare. Almost all quantity inferences you'll ever make are going to prove AT LEAST ONE (some / not all).
This would NOT work if I reversed the order.
All A's are B's.
Most B's are C's.
All Senators are rich.
Most rich people flaunt their wealth.
Does that mean that all / most / some Senators flaunt their wealth?
Nope. If there are 50,000 rich people in the world, then at least 25,001 of them flaunt their wealth.
But the 100 rich Senators discussed could easily be among the 24,999 rich people who don't flaunt their wealth.
Let me know if you're confused by any of this.
-
- JohnW106
-
Thanks Received: 0
-
Vinny Gambini
- Posts: 1
- Joined: February 20th, 2019
Re: Advanced Conditional Diagramming
"'Not all' just means "less than 100%", so 0% is still less than 100%.": "Not all" means "not every", and the logical opposite of "not all" is "all" or "any". You are stating that "not all" can include "none"? In this case its logical opposite would be "some", but the logical opposite of "not all" is "all" or "any". Please clarify. I think "not all" might include "none" but I am not sure.
3 posts Page 1 of 1