Imagine an experiment in which one student is selected at random from among all currently enrolled students in this university. Let A be the event that the selected student is classified as enrolled in engineering (one of the engineering schools), and let B be the event that the same student is currently enrolled in this class.
Express in set notations the following events.

1. The student is not in engineering:
2. The student is in engineering and in this class:
3. The student is not in engineering but in this class:
4. The student is not in engineering and is not in this class:
5. The student is either in engineering or is in this class:
6. The student is either in engineering or is in this class, but not both:

[tex]\left \{ x\varepsilon U;x\notin A \right \}[/tex], [tex]\left \{ x\varepsilon U;x \varepsilon A\cap B \right \}[/tex], [tex]\left \{ x\varepsilon U;x \notin A, x \varepsilon B \right \}[/tex], [tex]\left \{ x\varepsilon U;x \notin A, x \notin B \right \}[/tex], [tex]\left \{ x\varepsilon U;x \varepsilon A \cup B \right \}[/tex], [tex]\left \{ x\varepsilon U;x \varepsilon (B-A)\cup (A-B) \right \}[/tex]

Step-by-step explanation:

Set refers to the well defined collection of objects.

We can express a set in set-builder form or in roaster form.

Roster form is a mathematical representation of a set that lists all of the elements of the set within the curly bracket, separated by commas.

A set-builder notation is a mathematical representation for describing a set that lists all of the elements of the set by stating the properties that its elements must satisfy.

Let A be the event that the selected student is classified as enrolled in engineering (one of the engineering schools), and let B be the event that the same student is currently enrolled in this class.

Let U denotes the set of all students currently enrolled in the university.

1. [tex]\left \{ x\varepsilon U;x\notin A \right \}[/tex]

2. [tex]\left \{ x\varepsilon U;x \varepsilon A\cap B \right \}[/tex]

3. [tex]\left \{ x\varepsilon U;x \notin A, x \varepsilon B \right \}[/tex]

4. [tex]\left \{ x\varepsilon U;x \notin A, x \notin B \right \}[/tex]

5. [tex]\left \{ x\varepsilon U;x \varepsilon A \cup B \right \}[/tex]

6. [tex]\left \{ x\varepsilon U;x \varepsilon (B-A)\cup (A-B) \right \}[/tex]