Question

in an international food festival, jose can try foods from ethiopia, spain, and korea. 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 jose 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: List empty set

$\varnothing$

Step2: List single-country sets

$\{\text{Ethiopia}\}$, $\{\text{Spain}\}$, $\{\text{Korea}\}$

Step3: List two-country sets

$\{\text{Ethiopia}, \text{Spain}\}$, $\{\text{Ethiopia}, \text{Korea}\}$, $\{\text{Spain}, \text{Korea}\}$

Step4: List full set

$\{\text{Ethiopia}, \text{Spain}, \text{Korea}\}$

Answer:

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