There are a couple things to understand about the conjunctions/disjunctions.
The bitwise conjunctions (&, |, ^) can be used in place of boolean conjunctions (&&, and, ||, or, ^^, xor) most of the time in case you're a sloppy programmer, but be aware the two sets of conjunctions are not the same and will not necessarily yield the same results.
Consider the expressions if A & B and if A && B for example. The first example will be evaluated on a bitwise level, whereas the second will evaluate the truth of A and B. When GM evaluates the truth of an expression, any value less than 0.5 is evaluated to FALSE while anything higher is TRUE. It is important to understand that GM treats everything as numbers, so the expression A==B will return either a 0 or 1. What this means is something like A = B==C is valid syntax in GM (in which case A will be set to either 0 or 1). This is important to understand how a conditional of the expression if A & (B==C) actually works.
Consider the conditional if mouse_check_button_pressed(mb_left) & instance_position(mouse_x, mouse_y, obj_button). The first half will evaluate to either TRUE or FALSE, which as I said above is the set of possibilities {0,1}; the second half will evaluate to the set of possibilities {1000000,n} where n is however many instances have been created. Suppose the values you get are 1 and 1000000 respectively. In a conditional of the format if A && B, the result would be TRUE, since both expressions would evaluate to TRUE and the conditional is therefore if TRUE && TRUE. However, in a conditional of the format if A & B, the result would be FALSE: at the bitwise level 1 & 1000000 = 0, which is FALSE.
In short, be aware that if you do have a conjunction in a conditional and aren't getting the results you expected, make sure you didn't use a bitwise conjunction where you meant to use a boolean conjunction, and vice-versa. The two are nearly identical, but slightly different.
The two types of conjunction classes are also handled with different arithmetic priority as well. The bitwise conjunctions have higher priority than boolean conjunctions, meaning bitwise conjunctions will be processed before boolean conjunctions. So in the conditional if A && B & C, GM will first test the truthfulness of the bitwise expression B & C and then test the conjunction of the result with A. Also be aware it reads from left to right. Consider the conditional if A && B ^^ C and the conditional if A ^^ B && C. If A is TRUE, B is TRUE, and C is FALSE, then the first conditional will be TRUE (TRUE && TRUE is TRUE, TRUE ^^ FALSE is TRUE) but the second conditional will be FALSE (TRUE ^^ TRUE is FALSE, FALSE && FALSE is FALSE).
Anyway, in case you don't know your conjunctions, here is how they would work in a conditional:
& (bitwise AND)
Compares the bits of two values, returning TRUE if any set bits match
| (bitwise OR)
Combines the bits of two values, only returning FALSE if both values are 0
^ (bitwise XOR)
Compares the bits of two values, returning TRUE if any bits do not match
&& (boolean AND)
Compares the truthfulness of two values, returning TRUE if both values are TRUE
|| (boolean OR)
Compares the truthfulness of two values, returning TRUE if either values are TRUE
^^ (boolean XOR)
Compares the truthfulness of two values, returning TRUE if only one of the values is TRUE
For bitwise OR, I intentionally used "combines" instead of "compares", because I think it's a good way to treat bitwise OR. I didn't do the same for boolean OR because that makes it sound like contradictions are true (which may or may not be true).
