36) An electronic circuit contains three light bulbs, X, Y and Z, which are each either on or off at
any particular time. It is known that if bulb X is off or bulb Y is on, then bulb Z is on.
Which one of these statements necessarily follows from this?
A If bulb Z is on, then bulb X is off or bulb Y is on.
B If bulb Z is on, then bulb X is on and bulb Y is off.
C If bulb Z is on, then bulb X is on or bulb Y is on.
D If bulb Z is off, then bulb X is off and bulb Y is off.
E If bulb Z is off, then bulb X is on OR bulb Y is off.
F If bulb Z is off, then bulb X is on and bulb Y is on.
The answer is E yet I feel that the 'OR' needs to be an 'AND'
Why is E correct?