Resolving Truth Values

Both values known:

 T · T T · ⊥ T · ⊥ ⊥ · ⊥ T ⊥ ⊥ ⊥

 T ∇ T T ∇ ⊥ ⊥ ∇ T ⊥ ∇ ⊥ T T T ⊥

 T → T T → ⊥ ⊥ → T ⊥ → ⊥ T ⊥ T T

 T ↔ T T ↔ ⊥ ⊥ ↔ T ⊥ ­↔ ⊥ T ⊥ ⊥ T

At least one value unknown:

 T · ? ? · T ⊥ · ? ⊥ · ? ? · ? ? ? ⊥ ⊥ ?

 T ∇ ? ? ∇ T ⊥ ∇ ? ⊥ ∇ ? ? ∇ ? T T ? ? ?

 T → ? ? → T ⊥ → ? ⊥ → ? ? → ? ? T T T ?

 T ↔ ? ? ↔ T ⊥ ↔ ? ⊥ ↔ ? ? ↔ ? ? ? ? ? ?

Rules for Truth Functions

• A conjunction (dot) with a false conjunct is false.
• A disjunction (wedge) with a true disjunct is true.
• A conditional (arrow) with a false antecedent or a true consequent is true.
• A biconditional (double arrow) with a true component has the same truth value as the other component.
• A biconditional (double arrow) with a false component has a truth value opposite the other component.
• A conjunction (dot) is true only if ALL the conjuncts are true.
• A disjunction (wedge) is false only if ALL the disjuncts are false.
• A conditional (arrow) is false only if the antecedent is true AND the consequent is false.