Question

in an international food festival, keith can try foods from italy, spain, and ethiopia. he can choose to try foods from some, none, or all of these countries. in the braces below, list all the possible sets of countries whose food keith can try. write each set in your list in roster form. if there is more than one set in your list, separate them with commas. if you need the empty set in your list, use the symbol ∅.

Explanation:

Step1: Consider the empty - set

The empty - set represents the case where Keith tries no food, and it is written as $\varnothing$.

Step2: Consider sets with one element

The sets with one element are $\{\text{Italy}\}$, $\{\text{Spain}\}$, $\{\text{Ethiopia}\}$.

Step3: Consider sets with two elements

The sets with two elements are $\{\text{Italy},\text{Spain}\}$, $\{\text{Italy},\text{Ethiopia}\}$, $\{\text{Spain},\text{Ethiopia}\}$.

Step4: Consider the set with three elements

The set with three elements is $\{\text{Italy},\text{Spain},\text{Ethiopia}\}$.

Answer:

$\varnothing,\{\text{Italy}\},\{\text{Spain}\},\{\text{Ethiopia}\},\{\text{Italy},\text{Spain}\},\{\text{Italy},\text{Ethiopia}\},\{\text{Spain},\text{Ethiopia}\},\{\text{Italy},\text{Spain},\text{Ethiopia}\}$