Contrapositive is logically equivalent to the original sufficient -> necessary condition but it's flipped and negated.

Example:

If I am awake, I am running. A -> R

If I am not running, then I am not awake. /R-> /A

Logically, those are the same statements. If my necessary condition isn't met then my sufficient condition wasn't met.

Contrapositives are useful in chaining.

Example:

If I am awake, then I am running. A->R

If not awake, then I am sleeping. /A -> S

Therefore _____

As is, those don't chain together easily. But if I make premise 1 a contrapositive then I have

/R -> /A -> S

Therefore /R -> S

Negation is a logical contradiction. It's not the opposite, it's just shoving a 'not' (or removing a not in some cases) in front of the concept you're trying to negate. I find them useful in 'EXCEPT' question stems.

"If the above statements are true, each of the following statements could be true EXCEPT" is a really hard concept to keep in my brain when I'm moving down a list of choices. So I negate the "could be true" and turn "each" to "which".

"If the above statements are true, which of the following statements could be not true (or is not necessarily true)?" is an easier north star for me to navigate towards. It doesn't mean that I'm searching for a statement that's FALSE. I'm just looking for a statement that's not necessarily true.

@ryanmcamp01 Hi, English degree here. It’s really hard to boil down the English language like they attempt. A short answer is that in the provided sentence the predicate contains has a verb + noun that receives the action of the verb. So our core sentence needs both to keep the meaning. If the object and its modifier (fermented milk) were removed then it would be “my cat likes to drink”. What does it like to drink? Idk, whatever it gets from the Swedish cow. There’s way more to this but this should at least help. Happy to answer anything else.