Set Theory: Types of Sets, Unions and Intersections

The video tutorial introduces the concept of sets in algebra, explaining how they are used to define domains and express solutions to inequalities. It covers interval notation, including open, closed, and infinite intervals, and discusses set operations like intersection and union. The tutorial also explains the concept of empty and null sets, and demonstrates how to use sets and intervals to solve inequalities, including systems of inequalities.

What does the domain of a function represent?

• The range of possible outputs

• The set of all real numbers

• The set of all possible inputs

• The set of all integers

Which symbol is used to denote an open interval?

• Parentheses ()

• Curly braces {}

• Square brackets []

• Angle brackets <>

What is the intersection of two sets?

• The combination of all elements in both sets

• The elements common to both sets

• The set of all possible elements

• The difference between the two sets

How is the null set represented?

• A capital N

• A zero

• An empty pair of brackets

• A zero with a line through it

What is the solution to the inequality |x| > 2?

• x is greater than -2

• x is between -2 and 2

• x is greater than 2 or less than -2

• x is less than 2

In a system of inequalities, what does the solution represent?

• The union of all possible solutions

• The set of all real numbers

• The intersection of solutions for each inequality

• The difference between the solutions

What is the correct interval notation for x > -3 and x ≤ 4?

• [-3, 4)

• [-3, 4]

• (-3, 4]

• (-3, 4)