@Student101 Part 2 to follow up on these

All before Most

A->B-m->C

--

A<-s->C

• Wrong. Why? Lets imagine it like this. All 2 of my red cars are trucks. Most of my 100 trucks are made by ford. Therefore, some of my red cars are made by ford. I hope this helps to show were the gap is. The reason it's invalid is because we have no clue if some of my red cars are made by ford or not. Maybe 98 of my trucks (which would satisfy most) are made by ford and 2 of my trucks (the red ones) are made by 7Sage auto. Then yah we can't say that some of my red trucks are made by ford, because this is incredibly weak. It could be the change that my 2 red trucks are not part of that most that is made by ford.

All before Some

A->B<-s->C

--

A<-s->C

• Wrong. Why? Lets imagine it like this. All of my 3 cats are from London. Some cats from London enjoy drinking tea. Therefore, some of my cat's enjoy drinking tea. This is Invalid because what if for all we know my 3 cats from London are allergic of tea.

• Another way to think about it is like this. All A are B. Some B are C. Thus, some A are C. Think of it like exclusions and inclusions. Just because all of my A are now in B does not mean that some of those A's made it all the way to C. They could have been left behind and so we can't say that some A are C

I know that the lack of videos made this set a bit hard to understand so here are my explanations that helped me understand. They are super dumbed down because I am dumb so hope it helps

Sufficiency for Necessity

A->B

----

B->A

• WRONG. Why? Imagine this, All cats are mammals SO, all mammals are cats. Is this conclusion that all mammals are cats correct based off the premise that all cats are mammals. NO! The only thing the premise is telling us is that cats are mammals. We have no clue what mammals are and thus cannot say that mammals are cats because we would be confusing sufficient and necessity

Denying Sufficient Condition

A->B

/A

--

/B

• Wrong. Why? Just because we deny the sufficient condition does not mean that the necessary condition is false. Remember from the earlier lessons that, Membership in the subset is sufficient for membership in the superset, but it's not necessary.

• Example. All cats are mammals. Steve the lion is not a cat. Therefore, Steve the lion is not a mammal. Does the premise being true make the conclusion true? Is this valid? NO IT's NOT. All we know is that Cats are mammals. Steve the lion isn't a cat, ok cool that's fine, BUT does that mean he's not a mammals? We don't know. The premise doesn't tell us anything about Steve the lion not being a mammal.

Affirming the necessary condition

A->B

B

--

A

• Wrong. Why? Just because we say the necessary condition is true does not immediately mean that the sufficient condition is true. Remember back to subset and superset. The circle within the circle. Just because I'm in the first circle does that mean I'm in the second one? NO.

• Example. All cats are mammals. Steven the lion is a mammal. Therefore, Steve the lion is a Cat. Does this premise being true make the conclusion true? Is this valid? NO! Just because Steve the lion is a mammal tells us nothing about if he is a cat or not. Maybe to become a cat one needs to have stripes and Steve the lion doesn't have strips so we can't say that just because he satisfies the necessary condition that he is cool with the sufficient condition.

Most statement are not reversible

A-m->A

--

B-m->A

• Wrong. Why? Just because most A are B, does not mean most B are A.

• Example. Most cats are mammals. Therefore, most mammals are cats. Based off the premise of "most cats are mammals" can we say it's valid that most mammals are cats? NO WE CAN'T. We have no clue what most mammals are. All we know is that most cats are mammals

A->B-m->C

-----

A <-s-> C

• There could be a chance that all none of the A that are B were scooped into the C bucket when most B became C. So we cannot conclude that Some A are C

Back again with another explanation in hopes of it helping you because it might help me.

The key take away here: Don't read unidirectional arrows backwards

• Just because most A are B, does not mean most B are A

Example:

Most of the water I drink is freshwater. Therefore, most freshwater is drank by me.

Lawgic:

• Water I drink -m-> Freshwater

• -----

• Freshwater -m-> Drank by me

Is this valid? Does the premise being true make the conclusion true? NO! THIS IS INVALID.

Just because most of the water I drink is freshwater, DOES NOT MEAN that most of the freshwater is drank by me.

Just because most A are B, DOES NOT MEAN most B are A.

Ok so I also found this lesson confusing. What I think the key take away here is that just because the necessary condition is true tells us nothing about the sufficient condition. That's it.

My example:

All moms use the kitchen. I use the kitchen. Therefore, I am a mom

Lawgic:

• Moms -> use kitchen

• I KITCHEN

• --

• I MOM

This is Invalid. WHY? Because I'M NOT A MOM. I AM A SINGLE DUDE. Just because I am using the kitchen does that mean I am a mom? NO!

If you thought me using the kitchen meant I'm a mom you are confusing sufficiency for necessity. You are saying that using the kitchen is SUFFICENT for being a mom. you are saying "All those who use the kitchen are mom".

AFFIRMING THE NECESSARY CONDITION TELLS YOU NOTHING ABOUT THE SUFFICIENT CONDITION

All we know from the stimulus is that All moms use the kitchen.

Mom = Sufficient

Using kitchen = Necessary

If I affirm the necessary condition by saying "I use the kitchen" does that tell you anything about if I am a mom or not?

If the necessary condition is satisfied, it yields no information about the sufficient condition. The sufficient condition could be true or could be false.

Ok so I also found this lesson confusing. What I think the key take away here is that denying the sufficient condition tells you nothing about the necessary condition. That's it.

My example:

All students study at night. Timmy is not a student. Therefor, Timmy does not study at night.

• Lawgic:

  • Student -> Study at night

  • Timmy = /Student

  • --

  • Timmy = /Study at night

This is invalid. WHY? Because we have no clue when Timmy studies. All we know is that Timmy ain't a student.

Denying the sufficient condition by saying Timmy is not a student tells you nothing about the necessary condition of studying at night.

Membership in the subset is sufficient for membership in the superset, BUT IT IS NOT NECESSARY. There could be other subsets under the superset of "studying at night" and Timmy could be part of those other subsets.

Denying the sufficient condition (the subset) tells you nothing about the necessary condition (the superset)

How question 4 worked here.

Commercial airline pilots are required to have the ability to perform the “Lazy Eight” maneuver.

Most people who can perform the “Lazy Eight” maneuver enjoy flying.

• Statement 1

  • Airline pilot -> The lazy 8

• Statement 2

  • Lazy 8 -m-> Enjoy flying

• Conclusion

  • No valid conclusion. But my mistake was that I thought this meant airline pilots liked to fly

Why it is not valid

• What we know is that ALL airline pilots can do the Lazy 8.

• We also know that MOST people who can do the lazy 8 enjoy flying

• This is invalid because we have no clue if the pilots who can do the lazy 8 are part of the people who enjoy flying. Nothing here is telling us that all of those pilots who can do the lazy 8 enjoy flying. For all we know each one of those hates flying because the lazy 8 gives them a stomach ache.

Example to help understand:

This is like me telling you

• All of my friends are your friends,

• Most of your friends are your brothers friends

• SOOOOOO, does that mean my friends are now your brothers friends too?

  • NOPE. We have no clue here if my friends are also friends with your brother.

  • For all we know I could have only 1 friend, and that friend is with you, but you have 4 friends. The 3 friends who are not my friend could be friends with your bother. Hence, my one friend is not you brothers friend. Making it invalid to say that my friends are your brothers friends

All pens are black

• P -> B

Negated: Some pen's are not black

• P <-S-> /B

To negate all relationships we are saying "It' not the case that all pens are black".

What this does not mean is all pens -> /black. THIS IS A TRAP. All this negated statement means is that "Some pens are not black"

Does not matter specifically how much many is. All that is important to know is that many is more than some. Some can be at least 1 so just think about many being a bit more than that. BUT DON'T THINK MANY = MOST. WE DON'T KNOW IF MANY IS MOST. What we do know is that many is more than some

"Some" covers an intersect and that's why it can go both ways.

• Some cats are pets and Some pets are cats

  • These mean the same thing because they both have the same intersection in the middle where pets and cats overlap. Once you are in that intersection part in the middle you are part of both groups so it doesn't matter.

  • The word some means "at least one" so once I am in that middle group then yah, at least one cat is a pet, and at least one pet is a cat. Some can include all, sure. BUT it doesn't have to. All some has to do is mean "At least one"

  • Ex. I am a cat who is also a pet. I am in that middle intersection group so that means I can also say I am a pet who is a cat. On the flip lets pretend I am not a cat, but I am a pet. This means I can't be part of the that intersection in the middle. I am only part of the "pets" circle.

• Question 1)

  • X->Y > Z

    • I have to be in the Z superset to even be considered for the Y or Z subsets. Tom only has six months of training so he is not part of the Z superset. Since he is not part of Z there is no way he can be part of Y and since he can't be part of Y there is no way he could reach down to Z. If he wants to be able to reach Z he has to be part of Y, and to be part of Y he has to be part of Z.

  • Membership in the superset is not SUFFICIENT for membership in the subset.

• Question 2

  • Sentence 1 says Ok, First thing we need for the vote to not pass is senator Amidala to give her speech.

    • If speech -> /Vote pass

  • Sentence 2 with group 3 ruled applied Says, if Amidala delivers her speech, than the assassins failed

    • if speech -> assassination failed

  • Sentence 3 says. Yo, she wasn't on the ship where we were trying to kill her. What does this mean? That the assassination failed

    • Assassination Failed

  • Sentence 4, the conclusion says, Ok, based off all of this, the vote did not pass.

    Based off of this it's invalid because Valid means the conclusion follows when the premises are true. Here, we have no clue if the conclusion of the vote not passing follows. Hence, it is Invalid

Three different types of or

Inclusive or (and/or)

• You can use a pen or marker

Def: You can use just a pan, you can use just a marker, you can use both a pen and a marker

Exclusive or

• You must use a pen or marker, but not both

Def: You can use a pen, you can use a market, but you cannot use both. You must choose one or the other, not both

And

• The highlighter is better at marking than either the pen or the marker

def: The highlighter is better than the pen and the marker

It will snow, unless the clouds are blue

Step 1) Unless is the conditional indicator

Step 2) Identify the 2 conditions

• Condition 1: It will snow

• Condition 2: Unless the clouds are blue

Step 3:

• Condition 1: Snow

• Condition 2: Blue

Translation rule

Step 1) Select 1 of the ideas

• It will snow

Step 2) Negate the idea

• It will not snow

• /snow

Step 3) Make that the sufficient idea

• /snow -> blue

• It will not snow, unless the clouds are blue

Step 4) Take the contrapositive

• /blue -> Snow

• If the clouds are not blue, than it will snow

The thing that has helped me the best is trying to think of these are the subset/superset and then build the Lawgic based off of that.

Another thing I keep in mind is the idea that, membership in the subset in necessary for membership in the superset, BUT membership in the superset is not sufficient for membership in the subset.

Translation: If I am inside my room, I am also inside of my house (If I am in the subset, I am also in the superset).

BUT if I am in my house that does not mean I am in my room (If I am in the superset, that does not mean I am in the subset, there maybe some other door I need to enter before I can be in the subset)

Example of how I drew out the first 3 questions

Here's what helped me understand (This is for my own note taking, but feel free to enjoy if it helps)

The biggest thing that made the Kumar example click is the difference between subset and superset.

Sufficient conditions are the subset, and necessary conditions are the super set.

My translation: Membership in the subset is good enough (Sufficient assumption) for membership in the superset, but is not necessary (Necessary assumption)

Membership in the superset is necessary (necessary assumption) but it is not good enough (sufficient) to be apart of the subset.

My breakdown (Long winded, mainly for my self but feel free to read if it helps)

Suspect class is the sufficient condition here, and plaintiffs making a showing is the necessary condition.

Membership in the suspect class is sufficient to be part of the plaintiffs making a showing class, but it is not necessary as there are other ways that one can make a showing that the characteristic's defining the class is an immutable trait.

The reverse of this that helps me further understand is that: Membership in plaintiffs making a showing is necessary to be part of the suspect class (sufficient condition), but it is not good enough (sufficient) because there could be more things you need to check in order for you to get into that smaller bubble of the suspect class.

The second sentence is where we see the contrapositive of "X is not a member of set B". This is shown by the sentence saying "Plaintiffs have not cited any authority to support the conclusion that homosexuality is an immutable characteristic". Basically to be part of B we need to show that characteristic's defining the class are immutable, and then the second sentence say "well, you actually haven't shown any characteristic defining the class (homosexuality I think) as an immutable.

This is finally ties back into the final sentence in the form of "If not B (Superset) than not a member of A (Subset). How is this shown? The court basically said "oh you don't have membership in set B (the superset), so we cant give you membership into set A (The subset)

Membership in set B being characteristics to define the class as immutable, and membership in set A being to qualify as a suspect class

The bugs of the kingdom wanted to smell the flowers, others did not seek to go out and smell the flowers.

The bugs of the kingdom is the referent here (term being referred to)

"Others" is the negative referential

This example is showing that not those bugs of the kingdom wanted to go out and smell the flowers

For me the best way that I understood this is that the referential is the phrase that is in place for another phrase, the referent is the phrase that is being referred to. How do you know something is the a referential? You know it is a referential if it is a very broad term that is vague. You need the referent to understand what this broad and vague term is talking about.

Kernel: Cats will poop their pants

The best way for me to understand this was take the whole sentence and ask myself what matters. For question 1 the only details that mattered were "schools are not eligible".

Then when it comes down to identifying modifiers I ask myself "what kind". Schools, what kind of schools? Schools that fail to provide adequate facilities for physical education. For the next part of "are not eligible" I asked myself "for what?". are not eligible, for what? For the grant. This is how I broke things down for myself

Fish swim and cows eat.

Complex sentence since 2 clauses.

Clause 1: fish swim

Clause 3: cows eat