Question

Use a Venn diagram to answer the question.

At East Zone University (EZU) there are 683 students taking College Algebra or Calculus. 281 are taking
College Algebra, 456 are taking Calculus, and 55 are taking both College Algebra and Calculus. How many are
taking Algebra but not Calculus?

Answer 1

226 students take Algebra by not Calculus.

Explanation:

A Venn diagram is a graphical representation of sets. It visually demonstrates the common elements shared between different sets and the unique elements contained in each set.

Let set A represent the set of students taking Algebra.

Let set B represent the set of students taking Calculus.

Based on the given information:

• A = 281 (students taking Algebra)
• B = 456 (students taking Calculus)
• A ∩ B = 55 (students taking both Algebra and Calculus)

To represent the given information in a Venn diagram, draw two overlapping circles to represent the two sets.

The overlapping region represents the students taking both Algebra and Calculus. Therefore, place 55 in the overlapping region.

We are told that 281 students take Algebra. As 55 students take both subjects, to determine the number to place in the left part of set A (outside of the overlapping region), subtract 55 from 281:

• 281 - 55 = 226

We are told that 456 students take Calculus. As 55 students take both subject, to determine the number to place in the right part of set B (outside of the overlapping region), subtract 55 from 456.

• 456 - 55 = 401

The sum of the 3 regions is the total number of students.

• 226 + 55 + 401 = 682

The number of students taking Algebra but not Calculus is the left part of circle A, which is 226 students.