# Problem Solving Using Venn Diagrams

This trick or trap comes up a lot in combinatorics problems.It’s called “double counting.” To avoid this problem we can use Venn diagrams.This module contains three lessons that are build to basic math vocabulary.

Tags: Creative Writing Story PromptsBusiness Succession Planning DefinitionBest Place To Buy Cheap Paperback BooksDiving Into The Wreck ThesisSocial Work Courses UniversityDiscussion In Research PaperHolt Mcdougal Mathematics Course 1 Homework And Practice Workbook AnswersResistance Of A Wire Coursework GraphAnalytical Essay StructureAssignment On Entrepreneurship

MULTIPLES OF 3 AND NOT 5 OR 7: The number of elements in A = the integer part of (1000/7) – (9 19 38) = 142 – 66 = 76 Our final diagram: So the number of elements less than 1000 which are divisible by 3, 5 or 7 = 248 96 76 19 57 38 9 = 543 And the number of elements less than 1000 which are NOT divisible by 3, 5, nor 7 = 1000 – 543 = 457 The answer is (A).

Keep in mind I’m going to leave you with some challenging problems to try on your own.

All of these problems can be solved with Venn diagrams 1.

How many positive integers less than 1,000,000 are neither squares nor cubes? Given a random 6-digit integer, what is the probability that the product of the first and last digit is even?

Let’s agree the circle labeled A represents all the numbers less than 1000 which are divisible by 3.

The circle labeled B represents all the numbers less than 1000 which are divisible by 5.Let’s move from top to bottom: MULTIPLES OF 3 AND 5: Multiples of 3 and 5 are multiples of 15 The number of elements in A = the integer part of (1000/21) – 9 = 47 – 9 = 38 Now our diagram looks like this: Almost there…remember not to double count the portions of the diagram that are already labeled!Three worksheets to practice working with Venn Diagrams included in higher GCSE (9-1) examination.(Can be used with all boards, but questions taken from Edexcel or IB papers) 1.Because 3, 5, and 7 don’t share any factors, their least common multiple is the product of 3, 5, and 7: 105.To find the number of multiples of 105 less than 1000, we divide 1000 by 105.Problem Mat - print out on A3 double sided and you have a collection of Venn diagram questions students can attempt.Front page are simpler questions, with more challenging questions overleaf. Three past paper questions for students to attempt with solutions. A graduated mixture of past paper questions (levelled from warm to hot) plus a timed challenge of 5 questions to attempt.We have to careful about integers that are divisible by more than one of our numbers.For example, 21 is divisible by 3 and 7, but we can only count it once.

## Comments Problem Solving Using Venn Diagrams

• ###### Sets - Venn Diagrams - Building Blocks for Problem Solving.

Topics include ~Set theory, including Venn diagrams ~Properties of the real number line ~Interval notation and algebra with inequalities ~Uses for summation.…

• ###### The Problem with Cats and Dogs! - Project Maths

This lesson is designed to encourage younger students to use Venn diagrams as a problem solving tool and see that it has a purpose beyond.…

• ###### Sets and Venn diagrams - Australian Mathematical Sciences.

Before solving problems with Venn diagrams, we need to work out how to keep count of the.…

• ###### Problem-Solving Strategy Look for a Pattern; Use a Venn.

Develop and use the strategy Use a Venn Diagram. Plan and Compare alternative approaches to solving problems. Solve real-world problems.…

• ###### Venn Diagram Word Problems Passy's World of Mathematics

Let's start with an easy example of a two circle diagram problem. Here is a Video which shows how to solve Venn Diagram Survey Problems.…

• ###### Elementary set theory - Solve set problems without Venn diagrams.

So you don't need Venn diagrams, but you need to use the properties of. I think you cannot solve the problem without using set theory at all.…

• ###### GCSE 9-1 Venn diagrams by aliali Teaching Resources

Three worksheets to practice working with Venn Diagrams included in higher GCSE 9-1 examination. Problem Mat - print out on A3 double sided and you have a coll. 1. Problem Solving Toolkit - classroom display.…