The correct answer is 1

• First, we need to understand thatwhen there are novariables,there aretwo expressions :
  • False=0 and True=1
• For one variable p, four functions can be constructed. Afunction maps each input value of a variable to one andonly one output value.
  • TheFalse(p)function maps each value of p to0(False).
  • The identity(p)function maps each value of p to the identicalvalue.
  • The flip(p)function mapsFalsetoTrueandTruetoFalse.
  • TheTrue(p)function maps each value of p to1(True).
• For one variable:
  • ​4= \(2^{2^1}\),functions can be constructed.This information can be collected into a table:

  • Input	Function
    p	False	p	-p	True
    0	0	0	1	1
    1	0	1	0	1

• For n Variables:

  • Number of Variables	Number of Boolean Functions
    0	\(2^{2^0}\)= 20= 2
    1	\(2^{2^1}\)= 22= 4
    2	\(2^{2^2}\)= 24= 16
    3	\(2^{2^3}\)= 28= 256
    4	\(2^{2^4}\)= 216= 65536
    n	\(2^{2^n}\)

• Therefore, according to the above table, a maximum of 4 Boolean functions can be generated with 1 variable.