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Draw a Venn-diagram to show the relationship between two overlapping sets A and B. Now shade the region representing \[A\bigcup B\].

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Last updated date: 23rd Jul 2024
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Answer
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Hint: In this type of question we have to use the concept of set theory and Venn-diagram. In set theory we know that \[A \bigcup B\] represents the union of two sets A and B. As we have to draw a Venn-diagram first we will consider two circles which are the main part of the Venn-diagram. Now that two circles will represent two sets and as the sets are overlapping the two circles also overlap each other. Hence, we are going over the two circles so that we get a common region. Thus the region of two circles with a common region is we have to consider which has to be shaded.

Complete step-by-step solution:

Now we have to draw a Venn-diagram to show the relationship between two overlapping sets A and B and then shade the region representing \[A\bigcup B\].
We have given that there are two sets A and B so that first we consider two circles A and B which will represent the sets A and B.

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As we have given that the two sets are overlapping sets, so we are going to overlap these two circle now and hence we get,

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Thus this will represent the relationship between two overlapping sets A and B.
Now, we have to shade out the region which will represent \[A\bigcup B\]. We know that \[A\bigcup B\] means A union B which means the part consists of all the elements of A and all the elements of B. Hence we have to consider the entire region covered by both A and B and shaded accordingly.

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The above shaded region shows the required representation of \[A \bigcup B\].

Note: In this type of question students have to remember the definition of \[A\bigcup B\]. It includes both the region covered by set A and set B as the symbol in representation stands for union of sets. Also students have to note that the intersection of set A and set B denoted as \[A\bigcap B\] is represented by the common region between the two circles which is shown in the following Venn-diagram:
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So students have to take care related to union and intersection of two sets, they should not get confused with these two concepts and draw the correct Venn-diagram.