$3.$ Set Collection Operations and Concept Understanding

Based on the content of the Set interface in Java, answer the following questions:

$1)$ What is the definition of Set? Compared with List, what are the different characteristics of Set?

$2)$ The Set interface cannot be instantiated directly, and its two common implementation classes HashSet and TreeSet are usually used. Please explain the main differences between the two.

$3)$ Given the following code, answer the questions:

$```$

java

Set set$1=$ new HashSet;

set$1.$add$("$Alice$")$;

set$1.$add$("$Bob$")$;

set$1.$add$("$Charlie$")$;

Set set$2=$ new TreeSet;

set$2.$add$("$Bob$")$;

set$2.$add$("$David$")$;

set$2.$add$("$Charlie$")$;

$```$

a$.$ What is the result of set$1.$containsAll$($set$2)?$ Why?

b$.$ After set$1.$retainAll$($set$2)$ is executed, what elements are left in set$1?$ Please explain.

c$.$ Assuming that set$1.$addAll$($set$2)$ is used, what elements does set$1$ contain after execution?