Test each statement with a simple example instead of relying on definitions alone.
Take a book resting on a table. Gravity pulls down on it and the table pushes up on it with an equal and opposite normal reaction. Two nonzero forces are acting, yet the book is in equilibrium. This single example is enough to rule out statement (A), so it cannot be a valid conclusion.
Now think about what equilibrium actually requires for a rigid body in a plane, it must not accelerate in any direction, and it must not start rotating. Not accelerating horizontally means \(\Sigma F_x = 0\) (statement B). Not accelerating vertically means \(\Sigma F_y = 0\) (statement C). Not rotating means the net moment about any chosen point must vanish, \(\Sigma M = 0\) (statement D).
All three of these, taken together, are the textbook conditions for static equilibrium, and they must all hold simultaneously.
\[\boxed{\text{(B), (C) and (D) only}}\]