Someone explain the venn diagram for the logic equation A*(B+C) So, I am studying logic circuits and how to prove them with Venn diagrams. When drawing a Venn diagram for the equation A*(B+C) I figured it would look something like this:


But according to the answer key, and wolfram alpha, it looks something like this:


Can someone explain why this is? Because doesn't A*(B+C) simplify to AB + AC, which would only be the two shaded regions?
$(B+C) = B\overline{C}+\overline{B}C + BC$ 

and A with that and you get: 

$A*(B+C) = A*(B\overline{C}+\overline{B}C + BC) = AB\overline{C}+A\overline{B}C + ABC$ 

Remember that OR is the union and AND is the intersection.