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Truth Tables for Logical Operators: Conjunctions, Disjunctions, and Negations

Learn how truth tables define logical constants with conjunctions, disjunctions, and negations. Understand the truth values of compound sentences using AND, Inclusive OR, and Exclusive OR operations.

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Truth Tables for Logical Operators: Conjunctions, Disjunctions, and Negations

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  1. Conjunctions, Disjunctions, and Negations

  2. Truth Tables We use a truth table to define logical constants. A truth table lists all possible combinations of truth values for a particular constant. The left side of the table contains the truth values of the components of a sentence. The right side contains the truth value of the sentence.

  3. Negation Here’s the truth table for negation (~) P ~P T F F T This table lists all possible combinations of truth values for the sentence P.

  4. Conjunction “˄” In ordinary language the conjunction “˄” is AND. (also “but” and “moreover”) “˄” implies that a compound sentence will be truth IFF both sides are true, false otherwise. p q (p ˄ q) T T T T F F F T F F F F

  5. Disjunction “˅” The disjunction “˅” is an Inclusive OR. The resulting sentence is true if either or both sentences are true. p q p ˅ q T T T T F T F T T F F F

  6. Mutual Exclusivity Often “OR” is an Exclusive “OR” An Exclusive Disjunction (XOR), is true If and only if only one of the sentences is true. p q (p xor q) T T F T F T F T T F F F

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