In particular, what we do is the following. We interpret the values, the fractional values of the Boolean variables as a guide to the rounding scheme. In particular, we will assign a Boolean variable x(j) to true with probability x(j). While we will assign a variable to 0 with probability 1- x(j). Then it is possible to prove using some arguments that the probability that every clause is satisfied is at least 1 - 1 / z*(i). So, this means that we can relate the probability that the clause is satisfied to z*(i) that is the optimal fractional solution.

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