Question: Homework: 2.4 HW - Set Operations and Venn Diagrams with Three S
2.4.31
1 part | 0 of 1 point
Which regions represent set B\prime?
List the regions that represent set B\prime.
Graph shape: A rectangle labeled U contains three overlapping circles labeled A (left), B (right), and C (bottom) forming an 8-region Venn diagram. The regions are labeled I in A only, II in A \cap B only, III in B only, IV in A \cap C only, V in A \cap B \cap C, VI in B \cap C only, VII in C only, and VIII outside all circles. position_hint: center
1. **State the problem:** We need to find the regions that represent the complement of set $B$, denoted as $B'$. This means all elements in the universal set $U$ that are not in $B$.
2. **Recall the definition:** The complement of $B$, $B'$, includes all points outside the circle labeled $B$.
3. **Identify regions inside $B$:** The regions inside $B$ are:
- $II$ (intersection of $A$ and $B$ only),
- $III$ (in $B$ only),
- $V$ (intersection of $A$, $B$, and $C$),
- $VI$ (intersection of $B$ and $C$ only).
4. **Identify regions outside $B$:** These are all other regions:
- $I$ (in $A$ only),
- $IV$ (in $A$ and $C$ only),
- $VII$ (in $C$ only),
- $VIII$ (outside all circles).
5. **Conclusion:** The regions representing $B'$ are $I$, $IV$, $VII$, and $VIII$.
**Final answer:**
$$B' = \{ I, IV, VII, VIII \}$$