I was given the following boolean diagram:

I had to come out with the truth table and the simplified expression. I need help to check if my answers are correct below.

I was given the following boolean diagram:

I had to come out with the truth table and the simplified expression. I need help to check if my answers are correct below.

On
You've done a fine job on your truth table and in the simplification of $X$.
A quick way to check and show that your truth table is consistent with your simplification is to note, from the truth-table, that $X$ is true, or (1), in only one of the eight rows, when $A$ is false, and both $B, C$ are true.
This means $X$ holds exactly when $\overline A$ is true, AND $B$ is true, AND $C$ is true: $$X = \overline ABC$$.
I have verified it in EXCEL and see the answer below
TRUE = 1
FALSE = 0
Your relation is right and the truth table is right too
Thanks
Satish