Question

The logical sum of the all minterms in boolean function of n variablees

Answer 1

Answer:

1

Explanation:

Here is your answer

Variables a,b,c

To Prove: The logical sum of the all minterms in boolean function of n variable is 1.

Proof:

Here n=3

S= abc+ab'c'+ab'c+ab'c'+a'b'c'+a'b'c+a'bc'+a'bc

=ab(c+c')+ab'+(c+c')+a'b(c+c')+a'b'(c+c')

We know that,

(c+c')=1

=> ab(1)+ab'(1)+a'b(1)+a'b'(1)

=> ab+ab'+a'b+a'b'

=a(b+b')+a'(b+b')

Again, (b+b')=1

=>a(1)+a'(1)

=a+a'

=1

Hence proved..