Counting by complementis a technique for counting the number of elements in a set S that have a property by counting the total number of elements in S and subtracting the number of elements in S that do not have the property

Theprinciple of inclusion-exclusionis a technique for determining the cardinality of the union of sets that uses the cardinality of each individual set as well as the cardinality of their intersections.

1.Survey Results

Use the Inclusion/Exclusion Principle to determine the Cardinality of the Set

A survey of students revealed the following:

23 Students own at least one: XBOX ONE and a PLAYSTATION 4

10Students own both: XBOX ONE and a PLAYSTATION 423 Students owna PLAYSTATION 4 Determine: How many students own an XBOX ONE?

is it 3, 7, 10, or13

2. Counting Schedules

An instructor needs to schedule 3 GoToTraining sessions on any 7 days of the week.

How many schedules have sessions on a Monday or Friday (or Both)?

is it 35, 25, 15, or10