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Wikifunctions:Catalogue/Boolean operations

From Wikifunctions

These are the basic blocks from which to build logic states.

Boolean pairwise functions

2 nullary Boolean functions
Name ZID Value
nullary false nullary false (Z10206) F
nullary true nullary true (Z10210) T
4 unary Boolean functions
Name ZID F T
unary false unary false (Z10214) F F
identity Boolean identity (Z10215) F T
not not (Z10216) T F
unary true unary true (Z10217) T T
16 binary Boolean functions
Name ZID F ∗ F F ∗ T T ∗ F T ∗ T
binary false binary false (Z10257) F F F F
and and (Z10174) F F F T
not (A → B) not boolean implication (Z10962) F F T F
A Boolean left (Z10265) F F T T
not (B → A) not backwards Boolean implication (Z10964) F T F F
B Boolean right (Z10298) F T F T
xor Boolean inequality (Z10237) F T T F
or or (Z10184) F T T T
nor nor (Z10231) T F F F
xnor/eqv Boolean equality (Z844) T F F T
not B Boolean not right (Z10306) T F T F
B → A backwards Boolean implication (Z10348) T F T T
not A Boolean not left (Z10272) T T F F
A → B Boolean implication (Z10329) T T F T
nand nand (Z10243) T T T F
binary true binary true (Z10287) T T T T

Kleenean functions