Simplifying boolean expression

Say X= (((AB)’ (B+C)’)’ + C)’, to simplify, use DeMorgan’s theorem to get rid of the prime (NOT): X=(AB)’ (B+C)’ * C’

Then work on (AB)’ (B+C)’ = (A’+B’)(B’C’)=A’B’C’+B’B’C’=A’B’C’+B’C’=B’C'(A’+1)=B’C’

Now X=B’C’*C’=B’C’ or (B+C)’ if using DeMorgan’s theorem.

Verify this with multisim, the truth table of the logic is:

Simplify Boolean Logic circuit

Check the truth table, the only two 1’s output is due to B=0 and C=0 which is B’C’.

If you click the simplify button, you will see the simplified boolean expression under the truth table.