What are the applications of analog circuit and digital circuits?

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

Briefly answer the following questions: 
1. What is a digital signal?
2. Explain the function of modem in data communication.
3. Write two advantages of digital communication.

Draw the output signals $C_1$ and $C_2$ in the given combination of gates.