Question

The sum of all the minterms of a boolean function of n variables is equal to 1.

(a) Prove the above statement for n=3.
(b) Suggest a procedure for a general proof.

Answer 1

(a) Prove the above statement for n=3.
a'b'c' + a'b'c + a'bc' + a'bc + ab'c' + ab'c + abc' + abc = a'b' + a'b + ab' + ab = a' + a = 1.

(b) Suggest a general procedure for a general proof.
(Hint) For n > 3. If E represents the sum of all minterms of a function of n variables, then the sum of all minterms of a function of n+1 variables will be E(z'+z), which is equal to 1. This is obviously so for n = 4. Use induction for any n > 4.

BIBLIOGRAPHY: http://www2.cs.uh.edu/~jhuang/JCH/LD/chap02.html

Answer 2

Thanks you very much osanseviero. :)