Let's break down the problem based on the information provided in the image.

Given:

• A six-sided number cube (1 through 6) is rolled once.
• Two events are defined:
  • Event A: The number rolled is odd. So, $A = \{1, 3, 5\}$.
  • Event B: The number rolled is less than 4. So, $B = \{1, 2, 3\}$.

We need to determine the outcomes for:

1. (a) Event "A and B": The intersection of A and B, where both conditions are satisfied.

   • $A \cap B = \{1, 3\}$.

2. (b) Event "A or B": The union of A and B, where at least one condition is satisfied.

   • $A \cup B = \{1, 2, 3, 5\}$.

3. (c) The complement of the event A: All outcomes not in A.

   • The sample space for the cube is $\{1, 2, 3, 4, 5, 6\}$.
   • The complement of A, $A'$, includes numbers that are not odd: $A' = \{2, 4, 6\}$.

Answers:

• (a) Event "A and B": $\{1, 3\}$
• (b) Event "A or B": $\{1, 2, 3, 5\}$
• (c) The complement of the event A: $\{2, 4, 6\}$

Would you like further details or explanations? Here are some related questions to expand your understanding:

1. What is the probability of event "A and B" occurring?
2. How would the outcome set change if the cube had 8 sides instead of 6?
3. How can we use Venn diagrams to represent these events and their relationships?
4. What is the difference between independent and mutually exclusive events?
5. How do we find the complement of a compound event like $A \text{ or } B$?

Tip: Remember, the complement of an event includes all outcomes not included in that event within the sample space.