Lesson plan
Boolean function
and truth table of a ternary Boolean function In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {−1,1}). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f:\{0,1\}^k \to \{0,1\} , where \{0,1\} is known as the Boolean domain and k is a non-negative integer called the arity of the function. In the case where k=0 , the function is a constant element of \{0,1\} . A Boolean function with multiple outputs, f:\{0,1\}^k \to \{0,1\}^m with m>1 is a vectorial or vector-valued Boolean function (an S-box in symmetric cryptography). There are 2^{2^k} different Boolean functions with k arguments; equal to the number of different truth tables with 2^k entries. Every k -ary Boolean function can be expressed as a propositional formula in k variables x_1,...,x_k , and two propositional formulas are logically equivalent if and only if they express the same Boolean function.
Article summary
and truth table of a ternary Boolean function In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {−1,1}). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f:\{0,1\}^k \to \{0,1\} , where \{0,1\} is known as the Boolean domain and k is a non-negative integer called the arity of the function. In the case where k=0 , the function is a constant element of \{0,1\} . A Boolean function with multiple outputs, f:\{0,1\}^k \to \{0,1\}^m with m>1 is a vectorial or vector-valued Boolean function (an S-box in symmetric cryptography). There are 2^{2^k} different Boolean functions with k arguments; equal to the number of different truth tables with 2^k entries. Every k -ary Boolean function can be expressed as a propositional formula in k variables x_1,...,x_k , and two propositional formulas are logically equivalent if and only if they express the same Boolean function.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.