1. **State the problem:** We have two events from rolling a six-sided die: - Event E: "the number rolled is even" - Event T: "the number rolled is greater than two" We need to find the complement of each event. 2. **Recall the definition of complement:** The complement of an event includes all outcomes in the sample space that are NOT in the event. 3. **Identify the sample space:** The sample space for rolling a six-sided die is $\{1,2,3,4,5,6\}$. 4. **Find the complement of E:** - Event E includes even numbers: $\{2,4,6\}$. - The complement of E, denoted $E^c$, includes all numbers NOT in $E$. - So, $E^c = \{1,3,5\}$. 5. **Find the complement of T:** - Event T includes numbers greater than two: $\{3,4,5,6\}$. - The complement of T, denoted $T^c$, includes all numbers NOT in $T$. - So, $T^c = \{1,2\}$. 6. **Use the Venn diagram to verify:** - The universal set is $\{1,2,3,4,5,6\}$. - Numbers outside circle E are $E^c$. - Numbers outside circle T are $T^c$. This completes the process to find the complements of E and T.