I have a question regarding simplifying a circuit of a function below that has 5 logic gates in original.
f = (A + B) * (C + D) + (A + B) * (C + D)' + C
= (A + B) * ((C + D) + (C + D)') + C
= (A + B) * 1 + C Complement
= (A + B) + C
Now, I have reduced to 2 logic gates from 5. But, here, am I allowed to change (A + B) + C to A + B + C, so that I can reduce number of gates (i.e., 1 logic gate) even more? If I am allowed, is there a name for this process (what kind of law is this)?
Thank you in advance.