Q:

Listing the precedence order of the Boolean operators on java

My assignment is to list the precedence order of the Boolean operators, and to evaluate the following expressions:
true || true && false
true && true || false

However, I'm confused about what this means and how to do it. Can someone clarify what this assignment is asking for?

A:

To get an idea you can see below table. It shows all Java operators from highest to lowest precedence, along with their associativity

Taken it from here
So as you can see according to this, both results will be true

A:

Operator precedence is merely the order in which operations are applied. For example, consider the following mathematical statement:
10 + 6 / 2

Well, (10 + 6) / 2 = 16 / 2 = 8, but 10 + (6 / 2) = 10 + 3 = 13, so clearly it matters what order you perform the operations in. Mathematically, which one of these answers is correct? If you were asked this question on an exam, which answer should you put down? Operator precedence tells you that.
The question is asking you to do something similar for Boolean operators. 
Try the following program:
public class HelloWorld {

     public static void main(String []args){
        System.out.println(true || true && false);

        System.out.println(true && true || false);
     }
}

It turns out that both of them are true.
In order to learn more about this, you can experiment with parentheses to see how this changes the truth value of the statements. For example,
System.out.println((true || true) && false);

is false. Contrast that with the fact that 
System.out.println(true || true && false);

is true. What does this tell you about the order in which Java is performing the operations? Well, the way that I wrote the parenthesis changed the result, so clearly that's not right. You can infer from this that Java must be doing the parentheses "the other way":
System.out.println(true || (true && false));

If you check the chart in @Sand's answer, && does, in fact, have higher precedence than ||, so this operation is applied first. This is exactly what we see here.

