How To Solve Three Set Problem

Related Pages
Intersection Of Two Sets
Venn Diagrams
More Lessons On Sets

Venn Diagrams Of Three Sets

The intersection of three sets 10, Y and Z is the set of elements that are common to sets X, Y and Z. It is denoted by 10 ∩ Y ∩ Z.

Example:
Describe a Venn diagram to represent the relationship between the sets
X = {1, 2, 5, 6, 7, ix}, Y = {1, iii, 4, v, vi, 8} and
Z = {3, five, vi, 7, eight, 10}

Solution:
Nosotros detect that X ∩ Y ∩ Z = {v, 6}, 10 ∩ Y = {1, five, vi},
Y ∩ Z = {three, 5, 6, 8} and 10 ∩ Z = {5, 6, seven}

For the Venn diagram:
Pace 1: Draw three overlapping circles to represent the 3 sets.

Stride 2: Write downwards the elements in the intersection X ∩ Y ∩ Z.

Pace 3: Write down the remaining elements in the intersections:
10 ∩ Y, Y ∩ Z and Ten ∩ Z.

Step iv: Write down the remaining elements in the respective sets.
Notice that you lot first filling the Venn diagram from the elements in the intersection first.

Intersection of three sets

In full general, in that location are many means that three sets may intersect. Some examples are shown below.

How To Shade Regions Of Venn Diagrams Involving Three Sets

Venn Diagrams: Shading Regions with Iii Sets, Role ane of 2
This video shows how to shade regions of Venn Diagrams involving three sets.

Example:
Shade the indicated region:

(A ∩ B) ∩ C
(A ∪ B) ∩ C

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Venn Diagrams: Shading Regions with Three Sets, Part 2 of 2
More example to show to shade regions of Venn Diagrams involving three sets.

Example:
Shade the indicated region:
3) (A ∪ B)' ∩ C
4) (A' ∩ B') ∩ C'

Testify Video Lesson

How To Write An Expression For A Venn Diagram Region?
Create an expression to represent the outlines part of the Venn Diagram shown.

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How To Solve Word Problems With 3-Set Venn Diagrams?

Venn Diagram Problem With 3 Circles
Apply the given information to fill in the number of elements in each region of the Venn Diagram.
This video solves two problems using Venn Diagrams. I with two sets and ane with three sets.

Instance 1:
150 college freshmen were interviewed.
85 were registered for a math class
70 were registered for an English course
fifty were registered for both math and English

How many signed up just for a math grade?
How many signed upwardly only for an English course?
How many signed up for math or English?
How many signed up for neither math nor English language?

Case ii:
100 were students interviewed
28 took PE
31 took Bio
42 took Eng
9 took PE and Bio
10 took PE and Eng
6 took Bio and Eng
four took all 3 subjects
How many students took none of the three subjects?
How many students took PE, just not Bio or Eng?
How many students took Gio and PE merely not Eng?

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How To Solve A Venn Diagram Problem Involving Three Sets?
Example:
110 college freshmen were surveyed
25 took physics
45 took biology
45 took mathematics
10 took physics and mathematics
8 took biological science and mathematics
6 took physics and biological science
v took all 3
a. How many students took biology, only neither physics nor mathematics?
b. How many students took biology, physics or mathematics?
c. How many students did non take any of the three subjects?

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How to fill up a 3-circle Venn Diagram?
In this video we go over a basic discussion problem involving iii sets. We use a Venn diagram to answer the series of questions.

Bear witness Video Lesson

Venn Diagram Shading Calculator Or Solver
Enter an expression like (A Union B) Intersect (Complement C) to describe a combination of two or three sets and get the annotation and Venn diagram. Use parentheses, Union, Intersection, and Complement.

Try the free Mathway calculator and problem solver below to practice various math topics. Effort the given examples, or blazon in your own problem and bank check your answer with the step-by-pace explanations.
Mathway Calculator Widget

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