Question

THIS IS ONE QUESTION

[6] (5 points) There exist four Boolean functions of a single variable and 16 functions of two variables How many functions of 5 variables are there? Support your answer. How many functions of n variables are there? Support your answer.

Answer 1

A single variable has 4 boolean functions and 2 two variable has 16 functions.

Now,

The no. of boolean function with 5 variable are = 2^{2^n}

= 2^{2^5} (where, n is the no. of variable, i.e. n = 5)

=2³²

= 4294967296

The no. of boolean functions wit n variables are, = 2^{2^n}