Answered: . Construct a Venn diagram to…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.1: Counting

Problem 84E

See similar textbooks

Related questions

Question

100%

A. Construct a Venn diagram to represent your assigned problem. Include capital letter labels for all sets and indicate what each label represents.

B. Use the set notation symbols (∪,',∩) and set labels from part A to express each of the following sets:

• elements in both Group 1 and Group 2

• elements in Group 2 but not Group 1

• elements in Group 1 or Group 2

• elements in neither Group 1 nor Group 2

C. Determine the cardinality of each of the following sets, including an explanation of the process for how you determined the cardinality:

• elements in both Group 1 and Group 2

• elements in Group 2 but not Group 1

• elements in Group 1 or Group 2

• elements in neither Group 1 nor Group 2

Part 1 Transcript records of 2,538 college first-years were examined.
Let the following subsets be defined:
Group 1: the set of students who completed philosophy
Group 2: the set of students who completed chemistry
The records show 2,001 students completed philosophy and 1,064 students completed chemistry. The records also show that 1,333 of those who took
philosophy did not take chemistry.

Expert Solution

Step 1

The set symbols are represented below:

$\cup r e p r e s e n t s U n i o n \cap r e p r e s e n t s I n t e r s e c t i o n' r e p r e s e n t s C o m p l e m e n t$

Union describes the all elements of Either set A or Set B

Intersection describes the common elements of both set A and set B

Complement of set A describes the elements that are not in set A

The number of elements in a set is called Cardinality. For example, the number of elements in set A is called cardinality of A and is denoted as n(A).