2. (5 points) A safe has five locks, vw.x.y.z, all of which must be unlocked for

Question

2. (5 points) A safe has five locks, vw.x.y.z, all of which must be unlocked for the safe to open. The keys to the locks are distributed among five executives in the following manner: i. Mr. A has keys to v and x ii. Mr. B has keys to v and y ii. Mr. C has keys to w and y iv. Mr. D has keys to x and z v. Mr. E has keys to v and z o Determine the minimal number of executives required to open the case. o Find all combinations of executives that can open safe. Write an expression f(A,B,C,D,E) which d nl oes oaonat open safc. Winie an epresion tA B,cCDE) specifies when the safe can opened. who is the essential executive without whom safe cannot be opened?

Explanation / Answer

1. Minimal number of executives required are 3.

2.Combinations of executives who can open safe are:

f(A,B,C,D), f(A,B,C), F(B,C,D),F(A,B,C,D,E),F(C,D,E),F(B,C,D,E),F(A,C,D,E)

3.The essential executive is Mr. C

because the lock 'w' is only with executive Mr.C.

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