###### 1.

What do relations and mappings have in common?

###### 2.

What makes relations and mappings different?

###### 3.

State carefully the three defining properties of an equivalence relation. In other words, do not just name the properties, give their definitions.

###### 4.

What is the big deal about equivalence relations? (Hint: Partitions.)

###### 5.

Describe a general technique for proving that two sets are equal.