This first edition was written for Lua 5.0. While still largely relevant for later versions, there are some differences.
The fourth edition targets Lua 5.3 and is available at Amazon and other bookstores.
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3.3 – Logical Operators

The logical operators are and, or, and not. Like control structures, all logical operators consider false and nil as false and anything else as true. The operator and returns its first argument if it is false; otherwise, it returns its second argument. The operator or returns its first argument if it is not false; otherwise, it returns its second argument:
    print(4 and 5)         --> 5
    print(nil and 13)      --> nil
    print(false and 13)    --> false
    print(4 or 5)          --> 4
    print(false or 5)      --> 5
Both and and or use short-cut evaluation, that is, they evaluate their second operand only when necessary.

A useful Lua idiom is x = x or v, which is equivalent to

    if not x then x = v end
i.e., it sets x to a default value v when x is not set (provided that x is not set to false).

Another useful idiom is (a and b) or c (or simply a and b or c, because and has a higher precedence than or), which is equivalent to the C expression

    a ? b : c
provided that b is not false. For instance, we can select the maximum of two numbers x and y with a statement like
    max = (x > y) and x or y
When x > y, the first expression of the and is true, so the and results in its second expression (x) (which is also true, because it is a number), and then the or expression results in the value of its first expression, x. When x > y is false, the and expression is false and so the or results in its second expression, y.

The operator not always returns true or false:

    print(not nil)      --> true
    print(not false)    --> true
    print(not 0)        --> false
    print(not not nil)  --> false