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Drawing a Venn Diagram

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Use the information provided:

U={1,5,10,15,20,25,30}
A={1,10,15}
B={1,10,20,25}
C={5,15,30}

and use a venn diagram to determine wheather (A U B') U C= (A' U B) U C' for all sets A, B, and C. Show your work.

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A Venn diagram is constructed from given data. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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Venn diagram
Use the information provided

and use a Venn diagram to determine whether for all sets A, B, and C. Show your works.

Solution:
First, let us draw a Venn diagram containing sets A, B, C, and the universal set U as follows.

Next, consider each set and its compliment. For a better understanding, we will use colors to identify each set and its compliments in the Venn diagram.

Consider set A. The set A (containing 1, 10, and 15) is the blue rectangular blocks shown below.

Figure 1 Venn diagram with set A shown by the blue rectangular blocks

Its compliment, , can be easily seen as the rectangular blocks, which contain the numbers other than 1, 10, and 15. The diagram of is illustrated below.

Figure 2 Venn diagram with the ...

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