For each of the following problems, Create a conceptual data model, consisting of entity sets, relationships, attributes, and so on$,$ that can be used to answer questions similar to the questions given. Indicate cardinalities.

Questions:

$1.$ Assume the following problem is for a model for a university environment.

Which students are majoring in history? In English?

$2.$ Assume the following problem is for a model for a university environment.

How many faculty members are assigned to the math department? What are their names? Who is assigned to the music department?

$($Note: "math" and "music" are just examples of departments. Your model should also be able to answer these questions if$,$ say, sociology, political science, or mechanical engineering were substituted for math or music.$)$

$3.$ Assume the following problem is for a model for a university environment.

Which faculty members are teaching courses in sociology? Which courses are they teaching?

$4.$ Assume the following problem is for a model for a retailer.

Which products are priced above $$200?$ Which of these have a cost under $$150?$ Which come from manufacturers in the Midwest? What are the names of these manufacturers?