Someone explain the Venn diagram for the logic equation (A+B)(B+C)
The misunderstanding here is the same as in your previous question. If $B$ is true, the formula is true whatever the values of $A$ and&nbsp;$C$ are. This means that the whole of the $B$&nbsp;circle needs to be shaded.  Shading just the part at the top corresponds to saying "The formula is true if $B$ is true and $A$ and&nbsp;$C$ are both false." That is certainly true, but it's not the whole story.

For example, your proposed shading says that the formula is false if $A$ is true, $B$ is true and $C$ is false. But the formula is true in that case! You must shade every region of the diagram that makes the formula true. In this case, that means every region in the $B$ circle, and also the intersection of the $A$ and $C$ circles.  (Corresponding to, "The formula is true if $B$ is true, or if $A$ and $C$ are true, or both.")