Interval Notation and Compound Inequalities

This video tutorial introduces compound inequalities, explaining the concepts of intersection and union of sets. It provides examples of conjunctions and disjunctions, demonstrating how to solve compound inequalities using 'and' and 'or'. The tutorial includes graphing solutions on a number line and using interval notation. Special cases, such as no solution and all real numbers, are also discussed.

What is the intersection of two sets A and B?

• The set of elements in both A and B

• The set of elements in B but not in A

• The set of elements in A but not in B

• The set of elements in either A or B

In a compound inequality joined by 'and', what are we looking for?

• The difference of the intervals

• The intersection of the intervals

• The sum of the intervals

• The union of the intervals

How do you express an interval that includes 5 but not -2?

• (-2, 5]

• (-2, 5)

• [-2, 5)

• [5, -2]

What does a compound inequality joined by 'or' represent?

• The union of the intervals

• The intersection of the intervals

• The difference of the intervals

• The sum of the intervals

Which symbol is used to denote the union of two intervals?

• ⊇

• ⊆

• ∪

• ∩

What is the solution to a compound inequality with no intersection?

• All real numbers

• No solution

• The union of the intervals

• The intersection of the intervals

In a compound inequality with 'and', what happens if there is no overlap between intervals?

• The solution is the union of the intervals

• The solution is all real numbers

• There is no solution

• The solution is the intersection of the intervals

What is the solution to a compound inequality where the entire number line is covered?

• The intersection of the intervals

• The union of the intervals

• All real numbers

• No solution

How do you express all real numbers in interval notation?

• (-∞, ∞)

• [0, ∞)

• (-∞, 0]

• [0, 1]

In interval notation, what does a parenthesis indicate?

• The interval is finite

• The interval is infinite

• The endpoint is excluded

• The endpoint is included