Your logic expression can be simplified using Boolean Algebra.
Start with the given logic expression:
(ab + ac)'
Factor out a
:
(a(b + c))'
Apply De Morgan's law for negation of a conjunction:
a' + (b + c)'
Apply De Morgan's law for negation of a disjunction:
a' + b'c'
Therefore, output is true:
- anytime
a
is false, OR - when
b
is false ANDc
is false
Here is your truth table with corrections: