Convexity 1 - Homework 1

Undergraduate questions:

1. Lay Question 1.4
2. Lay Question 1.6
3. Lay Question 1.8
4. Lay Question 1.13
5. Lay Question 1.17
6. Lay Question 1.18
7. 

Additional graduate questions:

8. 
9. 
10. 

    For the last part of question 10, it's interesting to note that any set of constant width has the reuqired property (after scaling). For example the Reuleaux triangle is an appropriate example, as the following images show