Question

leila got a train ticket valid for three cities: madrid, prague, and london. she can choose to visit some, none, or all of these cities. in the braces below, list all the possible sets of cities that leila 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: List empty set

$\varnothing$

Step2: List single-city sets

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

Step3: List two-city sets

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

Step4: List three-city set

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

Answer:

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