Which of the following statements are true?

I. An event and its complement are mutually exclusive.

II. An event and its complement are exhaustive.

III. Any two mutually exclusive events are exhaustive.

IV. If $A \subset B$, then $A \cap B = A$.

Explanation

1. 01

   $E$ and $E'$ share no outcome (I) and together make up the whole sample space (II). If $A$ lies inside $B$, their common part is $A$ itself (IV).

2. 02

   III is false: on a die, $\{1\}$ and $\{2\}$ are mutually exclusive but leave out 3, 4, 5 and 6.