Question

there are nine train stations in a certain county. the blue line and red line are two train routes that pass through the county. here are some facts about the train stations.

• belen is a station along both the blue line and red line.
• ozark and utica are stations along the blue line but not the red line.
• arbor, dover, huron, and salem are stations along the red line but not the blue line.
• flint and provo are stations along neither the blue line nor the red line.

write each set in the indicated form.
(a) roster form: {belen, ozark, utica}
descriptive form: select
(b) descriptive form: the set of stations in the county not along the red line
roster form:
(c) descriptive form: the set of stations in the county along the blue line or the red line (or both)
roster form:

Explanation:

Step1: Match roster to description

Given roster {Belen, Ozark, Utica} matches stations only on Blue Line (plus Belen, which is on both).

Step2: Identify non-Red Line stations

Red Line stations: {Belen, Arbor, Dover, Huron, Salem}. Non-Red Line: All stations minus Red Line: $\text{Total stations} - \text{Red Line stations} = \{Belen, Ozark, Utica, Arbor, Dover, Huron, Salem, Flint, Provo\} - \{Belen, Arbor, Dover, Huron, Salem\} = \{Belen, Ozark, Utica, Flint, Provo\}$

Step3: Union of Blue and Red Lines

Blue Line: {Belen, Ozark, Utica}; Red Line: {Belen, Arbor, Dover, Huron, Salem}. Union combines unique stations: $\{Belen, Ozark, Utica\} \cup \{Belen, Arbor, Dover, Huron, Salem\} = \{Belen, Ozark, Utica, Arbor, Dover, Huron, Salem\}$

Answer:

(a) Descriptive form: The set of stations along the Blue Line
(b) Roster form: {Belen, Ozark, Utica, Flint, Provo}
(c) Roster form: {Belen, Ozark, Utica, Arbor, Dover, Huron, Salem}