2.3 True or false?

From arithmetic let’s turn to basic logic. Here there are only two values: true and false. We want to know what kinds of things we can do with one or two of these values.

The most interesting thing you can do to a single logical value is to replace it with the other. Thus, the not operation turns true into false, and false into true:

not true = false

not false = true

For two inputs, which I call p and q, there are three primary operations and, or, and xor. Consider the statement ‘‘We will get ice cream only if you and your sister clean your rooms.’’ The result is the truth or falsity of the statement ‘‘we will get ice cream.’’

If neither you nor your sister clean your rooms, or if only one of you clean your room, then the result is false. If both of you are tidy, the result is true, and you can start thinking about ice cream flavors and whether you want a cup...