Boolean Algebra Question (Logic Circuits)

I'm stuck on an engineering question about boolean algebra. I've been trying all day and asked my other students however I am still stuck. Could you please help me to draw a logic diagram and truth table for the Boolean expression "(A + B) . (A + C)". I also need to minimize the expression and do a logic circuit and truth table for it also.

I tried first attempt and got this: However I am not sure if it was right so I started researching and got this for my second attempt: I haven't completed the truth table, it's wrong I think. Could you guys comment on which attempt was the correct one, thank you!

My final attempt: Please tell me someone, is this finally correct? Both truth tables and logic diagrams?

• Welcome to the site. We do not mind helping if you show us what you have tried. Homework with no attempt at a solution is locked. Multiply it out and reduce. – StainlessSteelRat May 10 '17 at 13:51
• Try looking up "Distributive Law" – Andy aka May 10 '17 at 14:12
• And I looked up distributive law, Andy. Is there a certain method i'm supposed to follow when I minimise the expression for the second part of the question? Thank you! – TheBlackHat May 10 '17 at 14:28
• Given you were asked to draw a truth table first, it might be possible to derive the minimized expression right from it. There are many ways to minimize an expression. You should probably use the one taught in the classroom. – Eugene Sh. May 10 '17 at 14:29
• Sorry Eugene, I really do suck at boolean algebra as i'm new to it in Engineering. Please check my screenshot(s) and would it be possible for someone to tell me the first drawing/truth table is correct? – TheBlackHat May 10 '17 at 14:32

$$(A + B) \cdot (A + C)$$ Distributive. Multiply out terms. $$AA + AC + BA + BC$$ Idempotent $$A + AC + BA + BC$$ Distributive again. Seek common factors. $$A (1 + C + B) + BC$$ Annulment $$A + BC$$ Laws and Theorems of Boolean Algebra