22 lines
710 B
Markdown
22 lines
710 B
Markdown
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---
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categories:
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- Mathematics
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tags: [logic]
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---
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# Boolean functions
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An example of a Boolean function:
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$$
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f(x,y,z) = (x \land y) \lor (\lnot(x) \land z )
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$$
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Here is a work through where $f(1, 0, 1)$:
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- The first disjunction : $ \lnot(x) \land z $ is false because $x$ is 1 and $z$ is 1
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- The second disjunction: $x \land y$ is false because $x$ is 1 and $y$ is 0
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- The overall function returns true because the main connective is disjunction and one of the disjuncts (the second) evaluates to 1. Thus the output is 1.
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We can compute all possible outputs of the function by constructing a truth-table with each possible variable as the truth conditions and the output of the function as the truth value:
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