Question

ivanna got a train ticket valid for three cities: prague, athens, and madrid. she can choose to visit some or none, but not all, of these cities. in the braces below, list all the possible sets of cities that ivanna can visit. 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: Identify empty set

$\varnothing$

Step2: List single-city sets

$\{\text{Prague}\}$, $\{\text{Athens}\}$, $\{\text{Madrid}\}$

Step3: List two-city sets

$\{\text{Prague, Athens}\}$, $\{\text{Prague, Madrid}\}$, $\{\text{Athens, Madrid}\}$

Step4: Exclude full 3-city set

Omit $\{\text{Prague, Athens, Madrid}\}$

Answer:

$\varnothing$, $\{\text{Prague}\}$, $\{\text{Athens}\}$, $\{\text{Madrid}\}$, $\{\text{Prague, Athens}\}$, $\{\text{Prague, Madrid}\}$, $\{\text{Athens, Madrid}\}$