Verification of a solution to a mathematical logic problem

Premise.
b implies c
not-c or not-g
g or h
h implies not-c

Assume not-g. Thus
h; not-c: not-b.

Assune g. Thus
not-c: not-b.

Conclusion.
The cook and the butler are lying.
Either the cook or the handyman are telling the truth.
It cannot be determined if either of them are lying.


To get the same answer in a different way:

If you just start at the top and work forwards, Butler-true implies Cook-true (by 1) implies Gardener-false (by 2) implies Handyman-true (by 3) implies Cook-false (by 4), contradiction. So the butler is lying; moreover, the contradiction arose purely from an implication ("Cook-true") of Butler-true, so indeed the cook is lying too.

Then conditions 1, 2, and 4 become vacuous, and condition 3 is the only remaining restriction.

Tags:

Puzzle

Logic

Discrete Mathematics

Solution Verification

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