1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.