Question

(N) Northeast

(M) Midwest

(T) South

(W) West










(N) (M) (T) (W) Total

2009 (A) 0.9 1.2 1.9 1.2 5.2

2010 (B) 0.8 1.1 1.9 1.2 5.0

2011 (C) 0.8 1.1 1.9 1.1 4.9

Total 2.5 3.4 5.7 3.5 15.1


Use symbols to describe the given set.


The set of sales of existing homes in 2010 in the West and Midwest

Which one?


W ∩ (B ∪ M)


B ∪ (W ∪ M)


B ∩ (W ∪ M)


B ∩ (W ∩ M)


W ∪ (B ∪ M)


Compute its cardinality.

? million

Answer 1

• B ∩ (W ∪ M)
• 2.3 million

Explanation:

Apparently, these sets represent sales of existing homes. Then (values of) the homes sold in 2010 are those listed in set B.

The English wording "West and Midwest" doesn't actually mean homes that are categorized as both West and Midwest. There aren't any such homes, because these sets are mutually exclusive. That wording logically means "West or Midwest", so would represent the union W ∪ M.

Then the homes in W∪M that were sold in 2010 will be ...

B ∩ (W ∪ M) . . . . . matches the 3rd choice on the list

_____

The "cardinality" of a set is the number of elements in the set. Since the sets B and W and M are not shown, we cannot tell the cardinality.

Here, that word is apparently intended to mean the sum of the numbers designated as W and as M. For 2010, we have W=1.2, M=1.1, so ...

for 2010, W +M = 1.2 +1.1 = 2.3 . . . million