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Define a Boolean function $F(X_1, X_2, X_3, X_4, X_5, X_6)$ of six variables such that

$\\ \begin{array}{llll} F & = & 1, &  \text{when three or more input variables are at logic 1} \\ { } & = & 0, & \text{otherwise} \end{array} $
How many essential prime implicants does $F$ have? Justify they are essential.
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