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### What Is The Total Number Of Boolean Functions Possible Over N Boolean Variables?

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+1
$2^{2^{n}}$
0
Can you explain bit more? :)

+1 vote
Let's take 3 boolean variables for easy understanding .

a,b and c.

Each of the boolean variable can take 2 values , 0 and 1.

Thus total number of combinations possible for min terms = 2x2x2 = 8

And what are these? a'b'c' , a'b'c .... correct?

How to create boolean functions now ?

f(a,b,c) = Sum of min terms(you can also take Product of max terms , no issue :) ).

Each min term has two possibilities , either it can be in the function or not.

Thus total number of functions possible = $2^{Number of min terms}$ = $2^{2^{3}}$.

Similarly you can do it for n variables.
by Loyal (5.7k points)
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