Having extreme difficulty understanding conditional statements. everyone. I'm having a very difficult time understanding conditional statements, and was hoping someone could help me understand them.
I took discrete math this last spring and remember struggling with them, but at some point had to let go and just say &quot;it is what it is, I guess.&quot; I'm now taking a new course and conditionals are being thrown back in my face. I've watched several YouTube videos, read back over my discrete math textbook, did a google search and read the websites that came up in the first page and a half. Anything I do, I can't seem to grasp the meaning as a whole. Simply saying &quot;if p, then q&quot; or &quot;p implies q,&quot; or &quot;p is sufficient for q,&quot; or &quot;q if p&quot; does not make things clear.
I understand a conditional statement is a compound statement made of individual propositions that are either true or they aren't true. I can also see how compound statements such as &quot;It's raining outside AND it's cloudy&quot; could, as a whole statement, be true.
I've seen different definitions for what &quot;if p, then q&quot; mean, and they sometimes seem to contradict one another. So I'm going to ask it here. What is a conditional statement, and what does it mean?
Further, in a conditional statement:

Why does a true hypothesis and a true conclusion make the conditional true?
Why does a True hypothesis and a false conclusion make the conditional false?
Why does a false hypothesis and a true conclusion make the conditional true?
Why does a false hypothesis and a false conclusion make the conditional true?

Right now, I don't exactly know what questions I need to specifically ask to make it clear - all I know is I'm not getting it, and I'm exhausted with the run-around, lack of clarity, and simply not understanding. Hoping someone can help me.
Thank you and hope you're all well.
5.
Suppose that you’re told, If you score at least $85$ on the exam, you will get an $A$. There are four possibilities:

you score at least $85$ and get an $A$;
you score at least $85$ and don’t get an $A$;
you score below $85$ and get an $A$; or
you score below $85$ and don’t get an $A$.

Which of these outcomes contradict the statement? Certainly not the first one! The second one, however, definitely does: you scored at least $85$, but you did not get the promised $A$. Now what about the last two?
The thing to realize here is that taken literally, the statement says nothing about what will happen if you don’t score at least $85$; it merely promises you an $A$ if you do score at least $85$. In everyday contexts we generally don’t take such statements literally: we understand this one to mean (or at least very strongly imply) also that if you fail to score at least $85$, you will not get an $A$. But it does not actually say this, and in a formal logical context we interpret it literally. And since it says nothing about what will happen if you score below $85$, you can get any letter grade after scoring below $85$ without contradicting the statement: in that case there is nothing to contradict, because no prediction or promise was made. Since neither outcome — getting an $A$ or not getting an $A$ — contradicts it in this case, we say that it’s true.
In short, the truth values for these implications are based on the idea that the statement is false if and only if the facts actually contradict it. In the example that would be the case in which you scored at least $85$ but did not get the promised $A$. In general, for an implication $p\to q$, the only situation that absolutely contradicts it is the one in which $p$ is true, but $q$ is nevertheless false. It certainly isn’t contradicted when $p$ and $q$ are both true, and it makes no promises at all about $q$ when $p$ is not true.
There is one other difference between this logical implication and ordinary English usage. Ordinarily when we say that if $p$ is true, then $q$ is true, we are thinking of some causal connection between $p$ and $q$. In formal logic of the kind with which you’re dealing here we don’t care whether there’s any relationship between $p$ and $q$ at all: the truth value of the statement $p\to q$ is to be determined solely on the basis of the truth values of $p$ and $q$.
I'm not certain if this should be accepted as an answer, but I FINALLY found a video on YouTube that helped me understand things: https://www.youtube.com/watch?v=_uJ8rXDe6hs