Question

the results of a survey of customers at a pet supply store showed that 36 owned lizards, 26 owned geese, and 16 owned both lizards and geese. how many owned either a lizard or a goose? of the customers surveyed, \square owned either a lizard or a goose. (type an integer or a decimal.)

Explanation:

Step1: Recall the principle of inclusion - exclusion for two sets.

The formula for \( n(A \cup B) \) (the number of elements in either set \( A \) or set \( B \)) is \( n(A \cup B)=n(A)+n(B)-n(A \cap B) \), where \( n(A) \) is the number of elements in set \( A \), \( n(B) \) is the number of elements in set \( B \), and \( n(A \cap B) \) is the number of elements in both set \( A \) and set \( B \). Let \( A \) be the set of customers who own lizards and \( B \) be the set of customers who own geese. We know that \( n(A) = 36\), \( n(B)=26 \), and \( n(A \cap B)=16 \).

Step2: Substitute the values into the formula.

Substitute \( n(A) = 36\), \( n(B) = 26\), and \( n(A \cap B)=16 \) into the formula \( n(A \cup B)=n(A)+n(B)-n(A \cap B) \). So we have \( n(A \cup B)=36 + 26-16 \).
First, calculate \( 36+26 = 62 \). Then, calculate \( 62-16=46 \).

Answer:

46