Context for the puzzle:
You are on an island inhabited by knights and knaves. Knights always tell the truth, knaves always lie. You meet 5 natives:
Carl says "I am the same type as Peter".
Zippy says "Carl is a Knave or Jack is a Knight".
Jack says "I am a knight and Bill is a Knave".
Peter says "Bill is a Knight".
Bill says "I am a Knight and so is Carl"
From this, I have formulated the following equivalences:
- C ≡ P
- Z ≡ ¬C ∨ J
- J ≡ J ∧ ¬B
- P ≡ B
- B ≡ B ∧ C
I am trying to deduce which of the people are knights and which are knaves, however, after doing some substitution and manipulation using logical laws, I get to a point where I cannot make any more simplification and hence get stuck.
Could someone please point me in the right direction towards solving this problem?