# Level 2.1.4: All Six Operators

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#### The Logical Operator Rules Represented As Truth-Tables

 ~ P (P & Q) F T T T T F T T F F T F F F T T F F F F

 (P ∨ Q) (P x∨ Q) T T T T F T T T F T T F F T T F T T F F F F F F

 (P → Q) (P ↔ Q) T T T T T T T F F T F F F T T F F T F T F F T F

#### A Summary of the Logical Operator Rules

 Negation ~ Opposite of the truth-value of the WFF on the right. Conjunction & True when the WFF on the left and te WFF on the right are both true, otherwise false. Inclusive Disjunction ∨ False when the WFF on the left and the WFF on the right are both false, otherwise true. Exclusive Disjunction x∨ False when the truth-value of the WFF on the left matches that of the WFF on the right, true when they clash. Conditional → False when the WFF on the left is true and the WFF on the right is false, otherwise true. Bi-Conditional ↔ True when the truth-value of the WFF on the left matches that of the WFF on the right, false when they clash.

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