functionally complete

Propositional logics commonly use a set of logical connectives consisting of 5 elements: negation, conjunction, disjunction, implication and bijection, i.e. $\{NOT, AND, OR, IMPLY, IFF\}$.

Predicate logics commonly use the same symbols with addition of two quantifiers, $\{NOT, AND, OR, IMPLY, IFF, EXISTS, FORALL\}$

Although $IFF$ connective can be constructed from $IMPLY$ conectives, it is often included in the basic set of logical connectives because it lowers complexity of compound formulae; basically, it can be regarded as a mere shorthand.

In fact, many connectives can be descibed in term of others. A functionally complete set of logical connectives (Boolean operators) is the one which can be used to produce all other logical connectives. Such a set can express all possible truth tables by combining its elements into a Boolean expression.

A well-known functionally complete set is $\{AND,NOT\}$, consisting of binary conjunction and negation. Each of the singleton sets { NAND } and { NOR } is functionally complete.

IMPLY and AND connectives can be described in terms of OR connective - the minimum set of syymbols from which all other symbols can be constructed is