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Math Help - Boolean function?

  1. #1
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    Boolean function?

    Hi,i dont know how to form a Boolean function table.Can someone explain to me this picture http://uploadpic.org/storage/2011/Ry...M7MiRo1Q7v.png.
    How is this function f(x,y,z) obtained?
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  2. #2
    MHF Contributor
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    Re: Boolean function?

    Usually with truth tables one writes the rows of this table as columns and vice versa.

    Here, the columns list all possible triples (x, y, z) where each of the variables can be 0 or 1, from (0, 0, 0) to (1, 1, 1). Below each triple (x, y, z) is the value of the function f on (x, y, z). The function is built from conjunction ("and," written as juxtaposition, similar to multiplication), disjunction ("or," written as +) and negation ("not," written as postfix '). When x and y are 0 or 1, one can define conjunction of x and y as min(x,y), disjunction as max(x,y) and negation of x as 1 - x.

    For the function f(x, y z) to be 1, at least one of the disjuncts (connected by +) must be 1. Here each disjunct is 1 in exactly one column. For example, x'y'z' = 1 iff min(1 - x, 1 - y, 1 - z) = 1 iff 1 - x = 1 - y = 1 - z = 1 iff x = y = z = 0. Similarly, x'yz' = 1 iff x = z = 0 and y = 1. There are four disjuncts, and the function equals 1 in four columns.
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