document.write( "Question 1121053: In a group of students, 70 have a personal computers, 120 have a personal stereo and 41 have both. How many own at least one of these devices? Draw an appropriate Venn diagram. \n" ); document.write( "

Algebra.Com's Answer #736814 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Actually, the standard way to solve such problem is in one line as it is shown below:\r\n" );
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document.write( "    The number of those who own at least one of these devices = 70 + 120 - 41 = 149.\r\n" );
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document.write( "Intuitively, it is clear to you why I added 70 and 120, and only one aspect requires explanation: why I subtracted \"41\" ?\r\n" );
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document.write( "It is because when I added 70 and 120, I counted the common part twice.\r\n" );
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document.write( "After subtracting it, everything is in its right place.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Actually, you need Venn diagram only if you solve such problem at the first time.\r
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\n" ); document.write( "\n" ); document.write( "After that, the short solution presented above is totally enough.\r
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Counting elements in sub-sets of a given finite set\r
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\n" ); document.write( "\n" ); document.write( "Hello, Edwin !\r
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\n" ); document.write( "\n" ); document.write( "Thanks for your question.\r
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\n" ); document.write( "\n" ); document.write( "Regarding my preferences and answering your question, I prefer to use\r
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document.write( "    |A U B| = |A| + |B| - |AnB|     for two sets  A  and  B     and\r\n" );
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document.write( "    |A U B U C| = |A| + |B| + |C| - |AnB| - |AnC| - |BnC| + |AnBnC|     for  3  sets   A,  B  and  C.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is how I teach the students to solve the corresponding problems in my lessons\r
\n" ); document.write( "\n" ); document.write( "    - Counting elements in sub-sets of a given finite set\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on counting elements in sub-sets of a given finite set\r
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\n" ); document.write( "\n" ); document.write( "Also, it is how I solved numerous problems of this kind at this forum\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1116804.html\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1118494.html\r
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\n" ); document.write( "\n" ); document.write( "Everybody has his or her own taste and style in explaining such problems.\r
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\n" ); document.write( "\n" ); document.write( "I came from the culture (Math education culture) where the notion \"Venn diagram\" was totally unknown and was never used;\r
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\n" ); document.write( "\n" ); document.write( "NEVERTHELESS, the students (at least, advanced students) were able to solve such problems leaning on their logical skills,\r
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\n" ); document.write( "\n" ); document.write( "and I really prefer the students understand logic FIRST behind such problems.\r
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\n" ); document.write( "\n" ); document.write( "Then they will be able to solve the problems for four, five and so on sets and subsets   (where Venn diagrams become useless).\r
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\n" ); document.write( "\n" ); document.write( "It does not mean that I negate using Venn diagrams on the everyday basis.\r
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\n" ); document.write( "\n" ); document.write( "See THIS solved problem as another example.\r
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\n" ); document.write( "\n" ); document.write( "What I try to explain to students is the logic behind Venn diagram and the shortest and straightforward way to solve the problem.\r
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\n" ); document.write( "\n" ); document.write( "Thanks again for your question and the opportunity for me to highlight my point.\r
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\n" ); document.write( "\n" ); document.write( "P.S.   I also love and prefer compact formulas that speak by themselves and tell the entire and whole Math stories, as those listed above.\r
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