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 CHAPTER 9 Representations of Boolean Functions by Formulas

In Chapter 6, we used Boolean formulas to represent Boolean functions. The idea was to write a Boolean formula over a set of n variables and then assign 0-1 values to each variable. This assignment induces a truth value to the formula, and thus we have a Boolean function over n bits. In fact, any Boolean function can be represented by a Boolean formula if the set of connectives is complete. In Section 6.6, we proved that the set {¬, AND, OR} is a complete set of connectives.

In this chapter, we consider special representations of functions that are often called normal forms. Boolean formulas in a normal form are restricted forms of formulas.

Given a Boolean function, one may ...

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