# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.04

## Logic and Set Theory

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## The
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Venn Diagram
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In a Venn diagram there is a rectangle which shows the universal set. Circles within the rectangle show subsets of the universal set.

(figure available in print form)

If you have the universal set { 1,2,3,4,5} and Set A= {1,2,3} and set B = {3,4} then the two circles are shown to intersect since 3 is a member of both set A and set B. The diagram above shows the 3 where the circles intersect. Also shown are the 1 and 2 in A only and the 4 in B only. The number 5 is part of the Universal set but is neither an element of A or B.

Draw a Venn diagram to show the following:

1. U= {1,2,3,4,5}

A= {2,3}

B= {1,2,4}

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Solution:
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(figure available in print form)

2. U= { 2,4,6,8,12}

A= {2,6,4,12}

B= {2,12}

C= {6}

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Solution:
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(figure available in print form)

Sample lesson Plan 2 describes how the Venn diagram can be used to simplify problems dealing with intersection.

The use of diagrams can indeed make what appears to be a difficult problem rather easy. Students should be encouraged to use the Venn diagram as well as other pictures and charts to help make their word problems and problem solving easier and more meaningful.