By Cordelia Hall PhD, John O’Donnell BS, MS, PhD (auth.)
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Extra info for Discrete Mathematics Using a Computer
CHAPTER 1. INTRODUCTION TO HASKELL 14 2 and 3. Later in this book you will see a number of examples where it is useful to do this . Just as you can treat an operator as a function by putting parentheses around it, you can treat a function as an operator by putting single-quote characters around it. For example, the function max can be applied to two arguments in a function application: max 4 7. If you prefer, you can use it as an operator, like this: 4 t max t 7. 4 Function Definitions You can define new functions by giving the type declaration followed by the defining equation.
If the sun is cold, then the moon is made of green cheese. Here, A and B are both false, but the definition says that A why should the English translation of A ~ B be true? ~ B is true. 2. THE BASIC LOGICAL OPERATORS 43 Even though it may seem strange to you to define False -7 False to be True, you probably already understand the idea underlying the definition : it reflects a colourful way to express skepticism . Suppose, for example , that your friend claims 'Fifty people came to my party last night', but you're sure there were only twenty.
The usual notation in digital circuit design is to use 1 for True and 0 for False. Apart from being concise, this has the great advantage that 0 and 1 are more easily distinguishable than T and F, making the truth tables more readable. You may use any of these notations. However, if you use 0 and 1 as your notation for the truth values, be sure to remember that these are not numbers. For the sake of comparison, here is how the preceding truth table looks like with the 0, 1 notation. A 0 0 1 1 B A/\B 0 1 0 1 0 0 0 1 Given any two propositions, you can build a bigger one by connecting them with /\.