p
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
q
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
Statements
r
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
s
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
t
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
~p
Inverse of Statements
~q
~r
~s
~t
Facts: these are all true at the same time.
~q v p
~(~p -> r) ~r -> t
The 5 statements
p: study door locked
q: butler did it
r: maid did it
s: gardener did it
t: maid had mud on shoes
The four facts: which narrative statements match each of the
1. ~q v p
2. ~(~p -> r)
3. ~r -> t
4. ~s -> (q v ~t)
How to I know who did it??
Take a look at the truth table template.
All of the FACTS must be true at the same time.
Only one of the butler, maid, gardener can be true.
true at the same time.
~s -> (q v ~t)
atements match each of these?
he same time.
dener can be true.