Union of Events/Examples/Defective Devices

Examples of Unions of Events
Consider the experiment $\EE$ such that $3$ devices are checked as to whether they are operational.

Let $A$ be the event that at least $1$ of these $3$ devices is defective.

Let $B$ be the event that all $3$ devices are sound.

Then their union $A \cup B$ is a certainty.

Proof
Let $A$ occur.

Then it is not the case that all $3$ devices are sound.

Therefore $B$ does not occur.

Let $B$ occur.

Then it is not the case that at least $1$ device is defective.

Therefore $A$ does not occur.

Thus it is seen that:
 * $B = \overline A$

that is, $B$ is the complementary event to $A$.

Thus:
 * $A \cup B$

is the same thing as:
 * $A \cup \overline A$

and the result follows from Union of Event with Complement is Certainty.