Question: Let x1, x2, x3, x4 be binary variables and let z be some other binary variable. Formulate the logical operator by using integer linear programming,

Let x1, x2, x3, x4 be binary variables and let z be some other binary variable. Formulate the logical operator by using integer linear programming, i.e., write linear constraints so that

a) If all the xs take the value of zero, then z must take a value of 0.

b) z takes the value of 1 if all the xs take the value of 1.

c) If any x takes the value of zero, then z takes a value of 0.

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