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Level 2.1.4: All Six Operators

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.