# Logical Truth To show a statement A is 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.