You’re starting to see her as the enemy, which is also heartbreaking, because you’ve been friends for like 10 years!
Well, just hold on for a minute: Let’s organize the facts. You said you’re not sure if she knows how much you like him. After all, if she does know, then it might be time to find a new best friend, because she doesn’t care about your feelings. However, if she doesn’t know how much you like him (because you’ve been too embarrassed to admit it, perhaps?), then she’s not the enemy at all! These are two different situations entirely, and you now realize that you need more information before you jeopardize a lifelong friendship.
It’s really helpful to take the information we know and rewrite it into “if . . . then” statements, especially when the “if . . . then” logic is sort of hidden! These are called conditional statements.
General Statement

The same statement in
"if . . . then" form 

If he's late, I'll be mad.

If he's late, then I'll be mad.

My nails break when I travel.

If I travel, then my nails break.

I love the weather when it's rainy.

If it's rainy, then I love the weather.

All ducks are cute.

If it's a duck, then it's cute.

If your sister has been late for school every day this year, then you might guess that “your sister will always be late for school.” Or if you look at a bunch of prime numbers, like 3, 7, 19, and 41, you might try to conclude that “all prime numbers are odd,” which is totally false!
Deductive reasoning, on the other hand, means that we are told some general facts, called Givens, and we make specific conclusions based on them with a chain of “if . . . then” logic. This kind of reasoning is airtight (which means there could never be any counterexamples), and it’s what we’ll use when we do proofs.
Given: If it’s a baby duck, then it’s cute.
Given: If it’s cute, then Annie loves it.
Therefore: If it’s a baby duck, then Annie loves it.
Tada! We just did our first proof. That wasn’t so bad now, was it? By the way, even if you don’t agree that all baby ducks are cute (who are you?), because it was a “Given,” you have to act as if it’s true for the sake of this problem. Let’s make sure we remember the difference between induction and deduction, in case anyone asks (like on a test).
Given the statements below, use deduction to reach a new conclusion, if any. I’ll do the first one for you.
1. Given: Bonzo has a moustache. All monkeys have moustaches.
Answer: No conclusion possible
2. Given: All Barbies are dolls. All dolls are creepy.
3. Given: All puppies like bones. Sparky likes bones.
4. Given: All fruit grows on trees. All apples are fruit.
5. Given: All aliens speak Martian. Debbie speaks Martian.
(Answers at bottom)
The Converse, Inverse, and Contrapositive of a Statement
Let’s say we’re given All hot guys wear smelly socks. We could rewrite this as “If a guy is hot, then he wears smelly socks.” Great. Now, if we’re told that some guy (Zac) wears smelly socks, must he be hot? Nope! All sorts of people wear smelly socks, not just hot guys, after all. So the statement, “If a guy wears smelly socks, then he’s hot,” isn’t necessarily true. In fact, we’ve swapped the cause and effect in the statement, and that’s called the converse.
The converse, inverse, and contrapositive of a statement are all ways to change an “if . . . then” statement by moving around its “cause and effect” parts in very specific ways.
Converse: If q, then p.
Inverse: If not p, then not q.
Contrapositive: If not q, then not p.
Believe it or not, the contrapositive actually tells us the same information as the original statement. I mean, if a guy doesn’t wear smelly socks, then we know he can’t be hot . . . because if he were hot, then he’d be wearing smelly socks!
Same information, written differently!
Original statement ⇔ Contrapositive
In our particular case, the p is hotness and the q is smelly socks, right?
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