discrete mathematics and statistics applied in it

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In the country of Genovia, the president wants to ensure that the Monetary Committee can activate a device that opens the country’s safe. The safe system is to be activated by a device that obeys the following rules: Each member of the Monetary Committee has a button to push. The vice president or the president has a button to push (at least one of them—or both—have a button to push). The safe opens only if a combination of the president or the vice president (or both), and at least two of the committee members push the button. Complete the following: Set the exact constraints of the problem. Design the safe circuit. Complete the corresponding truth table. Explain your rationale on the creation of the safe circuit. Write the corresponding Boolean expression. Specify the input and output variables and the two states of each. Input: p = president’s button (1 = pushed, 0 = not pushed) vp = vice president’s button ( 1= pushed, 0 not pushed) x, y, z = Monetary committees’ buttons (1 = pushed, 0 = not pushed) Output: f = Safe lock (1 = open, 0 = locked)

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