Question

find the complement of A'B'C'+A'BC'​

Answer 1

Answer:

So we need to take the complement of ab+bc′+a′c+abc

(ab+bc’+a’c+abc)’

= (ab)’(bc’)’(a’c)(abc)’

= (a’+b’)(b’+c)(a+c’)(a’+b’+c’)

= (a’b’ + a’c + b’ + b’c)(ab’ + ac’ + a’c’ + b’c’ + c’)

= a’b’c’ + a’b’c’ + a’b’c’ + ab’ + ab’c’ + a’b’c’ + b’c’ + b’c’ + ab’c

Now we remove duplicates and simplify

= a’b’c’ + ab’ + ab’c’ + b’c’ + ab’c

= a’b’c’ + ab’ + b’c’

= ab’ + b’c’

= b’(a+c’)