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.

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

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