Explanation : 

Statement I: Anadyr in Siberia and Nome in Alaska are geographically close, separated by the Bering Strait and the International Date Line. The flight distance between Anadyr and Nome is approximately 813 km (500 miles). Anadyr is in the UTC+12 time zone, while Nome is in the Alaska Time Zone, which is UTC-9 during standard time (AKST) and UTC-8 during daylight saving time (AKDT). This significant time difference, spanning the International Date Line, means that when people are waking up and getting ready for breakfast in these cities, it would be different days. For example, a flight from Nome to Chukotka (where Anadyr is located) requires setting your watch 20 hours ahead. Therefore, Statement I is correct.

Statement II: Anadyr (UTC+12) is located west of the International Date Line, and Nome (UTC-8 or UTC-9) is located east of the International Date Line. Locations west of the IDL are typically a day ahead of locations east of the IDL. If it is Monday in Anadyr, Nome, being significantly behind in time and across the International Date Line, would be on the previous day, which is Sunday, not Tuesday. Therefore, Statement II is incorrect.