Can someone explain the logic diagram for the Boolean expression NOT A OR B AND C
The question is assuming that the operators precedence goes $NOT \rightarrow AND \rightarrow OR$, which is pretty standard for boolean logic.

Hence the proper parathensization would be $\text{((NOT A) OR (B AND C))}$, which correspods to the correct diagram, whereas the partial credits corresponds to $\text{(((NOT A) OR B) AND C)}$, which would just be a left to right evaluation of the operators.