The number of possible boolean functions that can be defined for n boolean variables over n valued boolean algebra is

Question

Q.86 The number of possible boolean functions that can be defined for $n$ boolean variables over $n$-valued boolean algebra is
(a) $2^{2^n}$
(b) $2^{n^2}$
(c) $n^{2^n}$
(d) $n^{n^n}$

Answer 1

answer is option (d)  n^n^n since n valued boolean algebra given.

we are familiar with the most common in computer science as 0,1 two valued so we have 2^2^n

if it is 3 valued boolean then no of functions would b 3^3^n

so similarly for n it is n^n^n

Answer 2

We know for n variable we have total 2^n combination are possible and these combination can have two values either 1 or 0 therefore we have 2^2^n that is option a

Answer 3

Number of rows in truth table =x = n^n

for each row 2 values are possible as it is boolean function= 2x2x2……...n^n times.

The number of possible boolean functions that can be defined for n boolean variables over n valued boolean algebra is 2^(n^n)