Does the 'if' statement work similar to 'PEMDAS' (math/parentheses)?

I believe the answer is a simple Yes, it is similar

Using your example

Anything inside the parenthesis will be considered one condition. You are clumping these conditions together. A simple comparison would be this (2+2) = (4) Same goes for bools. (true and false) = false while (false or true) = true

Lets say we have the following:

if (a and b) or c then
--Code
end

What this will do is check the first part of the conditional statement a and b. As you may already know, it will check to see if a and b are both true.

Although, because they are placed inside of parenthesis, they are considered a single condition.

If that turns out to be true, it will not bother checking the next condition because it has already succeeded regarding the or

Another example:

if (a and b) or (c or d) then
--Code
end

This gets a bit more tricky. It will check if a and b are both true. Either way, it will continue to the next condition because of the or

It would then check if c or d are true. If either of them are, the code will run through the statement as if true, regardless of what a and b resulted in.

A more numerical example:

if ((math.random(10) - 5) + 1 < (math.random(10) - 5) + 1) then
--Code
end

This will first follow PEMDAS and subtract 5 from the random number generated. Then it will add 1 to it afterwards. Which it would then compare to the same condition after the <and repeat the same process.

Does that answer any questions you had? If not, please let me know.

EDIT: To answer your comment, Yes. It will check things outside the parenthesis as long as the rest of the conditional allows it.

(a or b) and c will still check if c is true too because the statement relies on both conditions being true. Hence the and

Parenthesis are just a way to manipulate the data within the statements, but it will always go check the rest (Unless its an or of course)

PS: I know this is a rather hard topic to explain, was this ideal?