Liars and Truthtellers problem [duplicate]

Question

What would be the approach to a kind of problem that sounds like this:

A says B lies

B says C lies

D says B lies

C says B lies

E says A and D lie

How many lie and how many tell the truth? I am not looking for the answer to the problem above, but the approach to this kind of problem. Thanks a lot.

Answer 1

A -> !B
B -> !C
D -> !B
C -> !B
E -> !A & !D

Reminder:

X -> Y  <=>  !X | Y

Transform the 5 equations into logical propositions, and you will find answers.

Answer 2

To solve equations of the form

X₁ = NOT X ₃

X₅ = NOT X ₂

etc

Form a graph with nodes as X_i and connecting X_i and X _j iff the equation X_i = NOT X _j appears.

Now try to 2-colour the graph using Breadth First Search.