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The following table shows the number sales existing homes Mmons the different regions the United States during 2009 2011_ Take be the set of all home sales represen...

Question

The following table shows the number sales existing homes Mmons the different regions the United States during 2009 2011_ Take be the set of all home sales represented in the table and label the sets representing the home sales each rov colmn shown (s0 that; for example the set all sales existing homes Northeast during 2009-2011)_Northeast Midwest South (N) (M) 2009 (A) 2010 (B) 3 2011 (C) Total 2.5 3.4 5.7 Use symbols describe the given set: The set of sales of existing homes the Midwest 2009 M

The following table shows the number sales existing homes Mmons the different regions the United States during 2009 2011_ Take be the set of all home sales represented in the table and label the sets representing the home sales each rov colmn shown (s0 that; for example the set all sales existing homes Northeast during 2009-2011)_ Northeast Midwest South (N) (M) 2009 (A) 2010 (B) 3 2011 (C) Total 2.5 3.4 5.7 Use symbols describe the given set: The set of sales of existing homes the Midwest 2009 MUA West (W) Total 5.2 42 5.0 4.9 3.5 15.1 Man Mn MUW MaA Compute its cardinality. mmon



Answers

Home Sales Exercises are based on the following table, which shows the number of sales of existing homes, in millions, in the different regions of the United States during $2006-2008 .$ Take $S$ to be the set of all home sales represented in the table and label the sets representing the home sales in each row and column as shown (so that, for example, $N$ is the set of all sales of existing homes in the Northeast during $2006-2008$ ) Use symbols to describe each set, and compute its cardinality. The set of sales of existing homes in the Midwest in 2008

Okay here we have. The set of sales of existing homes in 2000 and seven is given by the set be in our table and the set of um sales in the south is given by the set T. So therefore the set of sales of existing homes in 2000 and seven excluding the sales in the south is going to be well be intersect T. Compliment, so be intersect complement. Um And then we have it in the table of the corresponding sets be anti compliments are colored and their overlap is going to be the set B intersect compliment. So then we have the cardinality of be intersect compliment is going to be equal to 1.0 plus 1.3 plus 1.1. So that's going to be equal to 3.4. And of course that's in billions.

Okay. So here we have the set of sales of existing homes in the northeast is given by the set n. And the set of sales in 2006 is given by the set a. So therefore the set of sales of existing homes in the northeast after 2006 is given by um we have an intersect a compliment And then we have that in our table. The corresponding sets and and a compliment are colored and the overlap is going to be while this setup and intersect compliment. So therefore the cardinality of an intersect a compliment or that's going to be equal to just 1.0 plus Um 0.8. That's equal to 1.8. And this is and millions. Yeah. Yeah.

Alright. So here we have the set of sales of existing homes in the west is given by the set W. And a set of sales of homes in the midwest is given by the set Emma. And the sales um in 2000 and seven is given by the set b. Therefore the set of sales of existing homes in 2000 and seven in the west and Midwest is going to be given by while it's going to be be intersect W. Union um be intersect. Okay. But we know this is also the same as by basically demorgans law here. This is giving the same thing as B intersect W. Um Union. Um Mhm. Mhm. Yeah. Okay. And then we have it in our table. The correspondent sets B. M. NW are colored and their overlap is going to be, well the set of be intersect W. Union M. So therefore the cardinality um of B intersect um W. Union M. Well that's going to be given by just 1.3 plus 1.1. So that's going to be 2.4 and we are in million. Okay. Yes.

Okay. So we have a given table and then we have here is a set of sales of existing homes in the south is given by the set T. And instead of sales of homes in the west is given by the set W. And the sales in 2000 and six is given by the set A. So therefore the set of sales of existing homes in the south and the west in the years other than 2006. Well that is going to be, we could either write this as a compliment intersects T. Union with a compliment intersect w. Or we could write that as a compliment. Uh Intersect the set T. Union W. All right. All right. And then we have it in the table. The corresponding sets T. W. And a compliment are colored and the overlap is going to be the set a compliment intersect T. Union W. So therefore the cardinality of that sets the cardinality of a compliment intersect T. Union W. Wow. That's going to be equal to 2.2 plus 1.8 Plus 1.1 plus 1.1. Which works out to be 6.2 and this is in millions. So this is equal to 6.2 million. Yeah.


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