# Functionally Complete Logical Connectives

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## Theorem

These sets of logical connectives are functionally complete:

### Negation, Conjunction, Disjunction and Implication

### Conjunction, Negation and Disjunction

### Negation and Conjunction

### Negation and Disjunction

### Negation and Conditional

### NAND

- $\set \uparrow$: NAND

### NOR

- $\set \downarrow$: NOR

There are others, but these are the main ones.

## Also see

- Functionally Complete Singleton Sets, in which it is seen that the only functionally complete singletons are $\left\{{\uparrow}\right\}$ and $\left\{{\downarrow}\right\}$.
- Functionally Incomplete Logical Connectives