$1$ PROBLEM $1$

$(40$ points$)$ On a warship, there are three officers and two captains. A vote is taken to decide whether to launch a missile. The missile is launched if the two captains agree. If the two captains disagree, the missile is launched if the three officers agree with launching. Design a digital circuit involving the smallest number of AND, OR$,$ and NOT gates that computes the final decision for voting policy. The easiest solution uses one OR gate with three inputs and three AND gates. Two of them have five inputs, and one has two inputs. Your solution should use, at most, the number of gates mentioned above.

Hint. Construct two small truth tables, one to compute the vote $V_0$ in the case two captains disagree, and the other to compute the vote $V_1$ when both captains agree. The solution is $V_0+V_1.$