A survey of 138 college students was taken to determine the musical styles they liked. Of those, 35 students listened to techno, 46 to hip hop, and 45 to rap. Also, 18 students listened to techno and rap, 13 to techno and hip hop, and 26 to hip hop and rap. Finally, 8 students listened to all three musical styles. Construct a Venn diagram and determine the cardinality for each region. Use the completed Venn Diagram to answer the following questions. a. How many listened to only techno music? $n($ only techno $)=12$ b. How many listened to hip hop and rap, but not techno? $\mathrm{n}($ hip hop and rap, not techno $)=$

Step 1 ：Given that the total number of students who listened to techno is 35, the number of students who listened to techno and rap is 18, the number of students who listened to techno and hip hop is 13, and the number of students who listened to all three genres is 8.

Step 2 ：We can find the number of students who listened to only techno by subtracting the number of students who listened to techno and another genre from the total number of students who listened to techno. This can be calculated as follows: \(35 - 18 - 13 + 8 = 12\).

Step 3 ：Similarly, to find the number of students who listened to both hip hop and rap, but not techno, we subtract the number of students who listened to all three genres from the total number of students who listened to both hip hop and rap. This can be calculated as follows: \(26 - 8 = 18\).

Step 4 ：Final Answer: \(\boxed{12}\) students listened to only techno music and \(\boxed{18}\) students listened to hip hop and rap, but not techno.