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Chapter 2.3, Problem 2TTO

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MATH IN OUR WORLD (LOOSELEAF)-W/AC...

3rd Edition
sobecki
ISBN: 9781259969690

Solutions

Chapter
Section
FindFindarrow_forward

MATH IN OUR WORLD (LOOSELEAF)-W/AC...

3rd Edition
sobecki
ISBN: 9781259969690
To determine

To sketch: A Venn diagram and shade the section AB.

Answer

A required Venn diagram as shown below.

images

Explanation

Step 1:

Draw a Venn diagram and name each area with a Roman numeral.

images

Step 2:

From the Venn diagram, list the regions that make up each set.

U={I, II, III, IV}, A={I, II} and B={II, III}.

Step 3:

Compute AB by using the sets in step 2.

The regions I and II are in A.

Therefore, the regions III and IV are not in A.

That is, the complement of A is III and IV.

That is, A={III, IV}.

The region II, III and IV are in either A or B, so these regions are in AB.

That is, AB={II, III, IV}

Step 4:

By step 3, shade the region II, III and IV as shown in below Figure 2.

images

From the Figure 2, it is observed that shaded regions represents AB.

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