Transcript Summary

Logical Truth
To show a statement A is a logic truth (tautology) ...
with a table:
The output row for A has all Ts.
with a proof:
Prove A.
with a tree:
The tree for -A closes.
Contradiction
To show a statement A is a contradiction ...
with a table:
The output row for A has all Fs.
with a proof:
Prove -A.
with a tree:
The tree for A closes.
Contingent
To show a statement A is contingent ...
with a table:
The output row for A has a F and a T.
with a proof:
No proof test is possible.
with a tree:
The tree for -A is open and
the tree for A is open.
Entailment
To show A entails B ...
with a table:
There is no A=T, B=F row.
with a proof:
Given A, prove B.
with a tree:
The tree for A, -B closes.
Equivalence
To show A is equivalent to B ...
with a table:
The output rows match.
with a proof:
Given A, prove B,
and given B, prove A.
with a tree:
The tree for A, -B closes
and the tree for B, -A closes.
Consistency
To show A and B are consistent ...
with a table:
There is a single row where
A and B are both T.
with a proof:
No proof test is possible.
with a tree:
The tree for A, B is open.