Ruby difference between &amp&amp, ||, and, or

As you may know in Ruby you can use boolean operators like:
&&, ||, !
additionally there are:
and, or, not
operators.

At first glance they are just synonyms of each other. But if look deeper there are slightly differences between them:
1. You cannot overwrite/overload operators &&, || but you can do this with and, or
2. More important difference is that &&, ||, ! operators have different precedence then and, or, not.
What does it mean in practice? Some examples:

#example 1
true || false && false #=> true

#example 2 
true or false and false #=> false

Those simple expressions look same, but results are different. Reason of it is different order of boolean checks. In first example && has higher precedence then ||, at first glance is fired check false && false and result of it is checked with ||. In second example boolean operators have same precedence, so boolean check is done from left to right what gives different result.

One more short example:

#example 3
a = true and  b = a  #=> true
puts a, b #=> true
              true

#example 4
x = true  && y = x  #=> nil
puts x, y #=>  nil
               nil

Again different results because of different precedences of operators - && has higher and and has lower to =. In example 3 firstly assignment had been made and after check with and, in example 4 in opposite way firstly boolean check was made. To make example 4 working as example 3 there is a need to introduce parenthesis:

(x = true)  &&  (y = x) #=> true
puts x, y #=> true
              true