Question

the greens are moving. their real estate agent located 79 houses listed for sale in their price range. of those houses listed for sale, 49 had a finished basement. 52 had a three - car garage. 37 had a finished basement and a three - car garage. complete parts a) through c). a) how many had a finished basement but not a three - car garage? 12 (type a whole number.) b) how many had a three - car garage but not a finished basement? (type a whole number.)

Explanation:

Step1: Define sets

Let $A$ be the set of houses with a finished basement and $B$ be the set of houses with a three - car garage. We know $n(A) = 49$, $n(B)=52$, $n(A\cap B)=37$ and the total number of houses $n = 79$.

Step2: Calculate number for part b

To find the number of houses with a three - car garage but not a finished basement, we use the formula $n(B\cap\overline{A})=n(B)-n(A\cap B)$.
Substitute the known values: $n(B) = 52$ and $n(A\cap B)=37$. So $n(B\cap\overline{A})=52 - 37$.
$52-37 = 15$

Answer:

15