General Claims and their Contradictories

General claims help determine if it is part of a collection or if it's separate. There are key words like All, Some, No, and Only.

All can be confusing because sometimes it means every single one with no exceptions and sometimes it means every single one with at least one exception. Some means at least one and is sometimes meant as "at least one, but not all."
No means not even one and is sometimes used by the word "only." Only means all are something, all have to be this.

Example of All: All cats meow.
Example of Some: Some people have black hair.
Example of No: No one is 300 years old.
Example of Only: Only people with bus passes can ride the bus.

The contradictory of each claim is one that makes it false.
Contradictory Examples:
All: Some cats don't meow.
Some: No person has black hair.
No: Someone is 300 years old.
Only: At least one person without a bus pass can ride the bus.
These contradictories make each claim on top false.

Again, this is exactly like discrete math when you negate a statement you get the contradictory of the statement.
All - some are not, not every
Some - No, all are not, not even one
Some are not - all are
No - some are
Only S are P - Some P are not S, Not every P is S