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? 15 (type a whole number.) c) how many had either a finished basement or a three - car garage? (type a whole number.)

Explanation:

Step1: Recall the principle of inclusion - exclusion

The formula for $|A\cup B|=|A| + |B|-|A\cap B|$, where $A$ is the set of houses with a finished basement and $B$ is the set of houses with a three - car garage.

Step2: Identify the given values

We know that $|A| = 49$, $|B|=52$, and $|A\cap B| = 37$.

Step3: Calculate $|A\cup B|$

Substitute the values into the formula: $|A\cup B|=49 + 52-37$.
$|A\cup B|=64$.

Answer:

64