How many Boolean expressions can be be formed with 3 Boolean variables?
Explanation
First, we need to understand that when there are no variables, there are two expressions :
False=0 and True=1
For one variable p, four functions can be constructed. A function maps each input value of a variable to one and only one output value.
The False(p) function maps each value of p to 0 (False).
The identity (p) function maps each value of p to the identical value.
The flip (p) function maps False to True and True to False.
The True (p) function maps each value of p to 1 (True).
For one variable:
Therefore, according to the above table, a maximum of 256 Boolean functions can be generated with
3 variables.
