Question

How to prove if a boolean function is functionally complete?

Answer 1

A set of operations is said to be functionally complete (or) universal if and only if every switching function can be expressed by means of operations in it.
The set {OR,AND,NOT} is clearly functionally complete.
The set {OR,NOT} is said to be functionally complete.
The set {AND,NOT} is also functionally complete.

Note:  A set is said to be functionally complete if we can derive a set which is already functionally complete 
 

Answer 2

A functionally-complete set of Boolean function consists of a set of Boolean functions from which you can construct all Boolean functions. { AND, NOT }, { OR, NOT }, {NAND }, {NOR} are four functionally-complete sets.