Consider four binary decision variables: 1, 2, 3, 4{0,1}. Suppose that the sum of these decision variables must be equal to an odd number. For instance, setting 1=1, 2=1, 3=1, and 4=0satisfies the condition while setting 1=1, 2=1, 3=0, and 4=0does not satisfy the condition. Derive a system of constraints, and potentially additional decision variables, that would eliminate all possible cases that do not satisfy the aforementioned condition.

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Consider four binary decision variables: X1, X2, X3, X4 E {0,1}. Suppose that the sum of these decision variables must be equal to an odd number. For instance, setting x1 = 1, X2 = 1, X3 = 1, and X4 = 0 satisfies the condition while setting x1 = 1, X2 = 1, X3 = 0, and X4 = 0 does not satisfy the condition. Derive a system of constraints, and potentially additional decision variables, that would eliminate all possible cases that do not satisfy the aforementioned condition