Level 2.1.4: All Six Operators
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The Logical Operator Rules Represented As Truth-Tables
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| ~ | P | (P | & | Q) | ||||
| F | T | T | T | T | ||||
| F | T | T | F | F | ||||
| T | F | F | F | T | ||||
| T | F | F | F | F |
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| (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 |
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| (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 |
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A Summary of the Logical Operator Rules
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| 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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Quizzes