Boolean functions

Let B={0,1}, then a f:B^k -> B function is called Boolean function, where B^k = BxBx...xB is Cartesian product. The k called the arity of function f, or in other words the number of arguments. It is simple to show that there are 2^(2^k) distinct Boolean functions of arity k. In previous post I mention some functions, so let define them precisely now.
The logical negation function ¬ has arity 1 and truth table is:

p	¬p
0	1
1	0

This function also written as ~ ,NOT and etc...

The logical conjunction ⋀ has arity 2 and truth table is:

p	q	p⋀q
0	0	0
0	1	0
1	0	0
1	1	1

Also written as &,*,AND and etc..

The logical conjunction ⋁ has arity 2 and truth table is:

p	q	p⋁q
0	0	0
0	1	1
1	0	1
1	1	1

Also written as +,OR and etc..

The logical implication → has arity 2 and truth table is:

p	q	p→q
0	0	1
0	1	1
1	0	0
1	1	1

There are 16 distinct Boolean functions of arity 2 and most of them have their own name, but they can be expressed with ,⋀,⋁ and →.In general the set of Boolean functions A called functionally complete if every Boolean function can be defined using functions of set A.
The set { ,⋀,⋁, →} of connectives is functionally complete, so every Boolean function can be written as a propositional formula. There are also other functionally complete sets, and such that sets which consists only one element. For example Sheffer's function (NAND,(p⋀q)) or NOR ((p⋁q)) are functionally complete. In general case the Post's theorem show which sets can be functionally complete.