### Question 4 #### a. Let $ U = \{ z \mid z \in \mathbb{Z} \} $, $ A = \{ z \mid z \text{ is an integer between 30 and 34} \} $, and $ B = \{ 29, 30, 31, 32, 33, 34, 35, 36 \} $. Draw the Venn diagram that represents $ U, A, $ and $ B $. Is $ A \subseteq B $ or $ B \subseteq A $? #### b. If $ R = \{ x \mid x \text{ is an odd, positive integer and } x < 12 \} $ determine the number of subsets contained in $ R $ and the number of proper subsets. ### Explanation #### Venn Diagram The Venn diagram for part (a) is not shown, but here's an explanation: - **Universal Set ($U$)**: Contains all integers. - **Set $A$**: Includes integers 30 through 34. - **Set $B$**: Contains integers 29 through 36. - **Relationships**: Check whether all elements of $A$ are in $B$ (i.e., $A \subseteq B$), and whether all elements of $B$ are also in $A$ (i.e., $B \subseteq A$). #### Subsets of $ R $ For the set $ R = \{ 1, 3, 5, 7, 9, 11 \} $, we have: - **Number of Elements**: 6 - **Total Subsets**: $ 2^6 = 64 $ - **Proper Subsets**: 63 (since proper subsets exclude the set itself)

### Question 4 #### a. Let $ U = \{ z \mid z \in \mathbb{Z} \} $, $ A = \{ z \mid z \text{ is an integer between 30 and 34} \} $, and $ B = \{ 29, 30, 31, 32, 33, 34, 35, 36 \} $. Draw the Venn diagram that represents $ U, A, $ and $ B $. Is $ A \subseteq B $ or $ B \subseteq A $? #### b. If $ R = \{ x \mid x \text{ is an odd, positive integer and } x < 12 \} $ determine the number of subsets contained in $ R $ and the number of proper subsets. ### Explanation #### Venn Diagram The Venn diagram for part (a) is not shown, but here's an explanation: - Universal Set ($U$): Contains all integers. - Set $A$: Includes integers 30 through 34. - Set $B$: Contains integers 29 through 36. - Relationships: Check whether all elements of $A$ are in $B$ (i.e., $A \subseteq B$), and whether all elements of $B$ are also in $A$ (i.e., $B \subseteq A$). #### Subsets of $ R $ For the set $ R = \{ 1, 3, 5, 7, 9, 11 \} $, we have: - Number of Elements: 6 - Total Subsets: $ 2^6 = 64 $ - Proper Subsets: 63 (since proper subsets exclude the set itself)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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