Assume that the following were Newspaper reports on a serious incident that occurred in a secondary school yesterday: ¡°in one of the modern classrooms all the window glasses were broken¡±. Four students are suspected ¨C Lizzy, Dimson, Tonia and Micheal. Consequently, they were all cross-examined and each gave three statements as follows:
Lizzy
a.I am not the one (L1)
b.I never went to the window (L2)
c.Micheal knows, who broke it (L3)
Dimson
a.I didn¡¯t break the glasses (D1)
b.I never knew Micheal before I came to this school (D2)
c.Perhaps, Tonia did it (D3)
Tonia
a.I didn¡¯t (T1)
b.Micheal did it (T2)
c.Dimson was lying, saying that I did it (T3)
Micheal
a.Not me!(M1)
b.Lizzy broke the glasses (M2)
c.Dimson can ascertain for me, since he knew me from my birthday (M3)
If you were called to investigate this matter and assume that one of the three statements made by each above was false. Write the Boolean expression and minimize the resulting system equations to determine who broke the glasses.

Solution:

This is how I started the solution;

L = L1'L2L3 L1L2'L3 L1L2L3'

D = D1'D2D3 D1D2'D3 D1D2D3'

T = T1'T2T3 T1T2'T3 T1T2T3'

M = M1'M2M3 M1M2'M3 M1M2M3'

where L = Lizzy's statements
D = Dimson's statements
T = Tonia's statements
M = Micheal's statements

Please, I am stuck here I need your help. Thanks

 

It's a pretty poorly contrived problem, but let's go with it.

Each student made three statements.

Each student basically made the statement "I didn't do it!"

The claim is that each student has made exactly one false statement.

What does that mean about the statements made by the student that actually did it?

Are there sets of statements that you can group together and say that they are mutually exclusive (i.e., they can't both be true)?