&, | , &&, || what…?

A friend of mine was wondering the advantage over the various operators.  I used the wording short circuits and thus does not eval the portion of the op to the right.

I sent her to this documentation site…

&& and || Operators

• To avoid exceptions and increase performance by skipping unnecessary comparisons, use && instead of & and || instead of | when you perform comparisons, as shown in the following example.
  C#

              Console.Write("Enter a dividend: ");
              var dividend = Convert.ToInt32(Console.ReadLine());
  
              Console.Write("Enter a divisor: ");
              var divisor = Convert.ToInt32(Console.ReadLine());
  
              // If the divisor is 0, the second clause in the following condition
              // causes a run-time error. The && operator short circuits when the
              // first expression is false. That is, it does not evaluate the
              // second expression. The & operator evaluates both, and causes 
              // a run-time error when divisor is 0.
              if ((divisor != 0) && (dividend / divisor > 0))
              {
                  Console.WriteLine("Quotient: {0}", dividend / divisor);
              }
              else
              {
                  Console.WriteLine("Attempted division by 0 ends up here.");
              }