Truth Table Generator info

Truth Tables in Propositional Logic are a systematic method for evaluating and representing the truth values of logical formulas. In this app, you can generate truth tables for propositional logic. You can join premises with an AND operator and use Implication for the conclusion.

For more detailed information, see Wikipedia

See Truth Table Generator here

Input Syntax

Use of both uppercase and lowercase alpahabets as predicates is allowed, although they would be treated as different predicated.

• Conjunction (And Operation): The operator for conjunction is represented by the symbol "∧" or "&". It combines two propositions and is true only when both propositions are true.
  Example: P ∧ Q, A & B
• Disjunction (Or Operation): The operator for disjunction is represented by the symbol "∨" or "|". It combines two propositions and is true when at least one of the propositions is true.
  Example: P ∨ Q, A | B
• Material Implication: The operator for material implication is represented by the symbol "->. It represents "if...then..." statements and is true unless the first proposition is true and the second is false.
  Example: P -> Q
• Biconditional: The operator for biconditional is represented by the symbol "<->". It represents "if and only if" statements and is true when both propositions have the same truth value.
  Example: P <-> Q
• Negation: For the operator of negation, the symbols "~", "!", and "¬" are permissible. It is used to reverse the truth value of a proposition.
  Example: ~P, !(P -> Q), ¬R

Supported Rules

• Negation Rule

  The Negation Rule is used to determine the truth value of a negated proposition. It negates the truth value of the proposition it applies to. If the original proposition is true, the negation is false, and if the original proposition is false, the negation is true.

• Conjunction Rule

  The Conjunction Rule is used to determine the truth value of a conjunction (AND) between two propositions. It evaluates to true only if both of the constituent propositions are true; otherwise, it is false.

• Disjunction Rule

  The Disjunction Rule is used to determine the truth value of a disjunction (OR) between two propositions. It evaluates to true if at least one of the constituent propositions is true; otherwise, it is false.

• Implication Rule

  The Implication Rule is used to determine the truth value of an implication (→) between two propositions. It evaluates to false only if the antecedent is true and the consequent is false; otherwise, it is true.

• Biconditional Rule

  The Biconditional Rule is used to determine the truth value of a biconditional (↔) between two propositions. It evaluates to true if both propositions have the same truth value (either both true or both false); otherwise, it is false.