The complete calendar for the year 2013 is being compared with previous and later years. Among the following options, for which year is the calendar exactly the same as that of 2013?

Introduction / Context:
Calendar repetition questions require you to understand when the pattern of weekdays and dates repeats. Two years have the same calendar when every date falls on the same weekday. This happens only when both years share the same leap year status and when the starting weekdays align after accounting for shifts caused by intervening years.

Given Data / Assumptions:
- Reference year = 2013. - Candidate years = 1998, 2017, 2009, 2002. - Gregorian calendar leap year rules apply. - We need to identify which candidate year has the same day date layout as 2013.

Concept / Approach:
Two years share the same calendar if they are either both leap years or both normal years and the total weekday shift between them is a multiple of 7. A normal year causes a 1 day shift for the next year, and a leap year causes a 2 day shift. Because 2013 is a non leap year, only non leap years can match it exactly. We then consider the cumulative shifts of weekdays between 2013 and each candidate year to find where the alignment repeats.

Step-by-Step Solution:
Step 1: Check if 2013 is a leap year. It is not divisible by 4, so 2013 is a normal year. Step 2: Evaluate leap year status of candidates: - 1998: non leap year. - 2017: non leap year. - 2009: non leap year. - 2002: non leap year. Step 3: Since all candidates are non leap years, we must distinguish them based on day shifts. Step 4: Consider years between 2002 and 2013 to see if the starting weekday repeats. Between 2002 and 2012 inclusive, count leap years and normal years. Step 5: Leap years between 2002 and 2012 are 2004, 2008, and 2012, making 3 leap years. Step 6: Number of normal years in that span is 8 (2003, 2005, 2006, 2007, 2009, 2010, 2011, plus 2002 or 2012 depending on precise boundaries), leading to a total shift which accumulates to a multiple of 7 days. Step 7: The net effect is that 2002 and 2013 start on the same weekday and, because both are non leap years, every month layout is identical. Step 8: Direct comparison of month wise calendars or using a verified day of week algorithm confirms this match.

Verification / Alternative check:
One alternative is to use a known calendar for 2002 and check a few key months such as January and February against 2013. If 1 January of each year falls on the same weekday and the leap year structure matches, the entire calendar will match. Practitioners and standard tables show that 2002 and 2013 indeed have identical day date patterns, validating that they share the same calendar.

Why Other Options Are Wrong:
- Although 1998, 2009, and 2017 are also non leap years, their 1 January weekdays differ from that of 2013, so the monthly layouts shift. - This means some dates, such as 1 March or 15 August, fall on different weekdays compared with 2013.

Common Pitfalls:
Students sometimes assume a fixed repetition cycle (for example every 11 or 28 years) without taking into account the specific arrangement of leap years. Others focus only on whether the year is leap or not and forget to check the starting weekday. For examination questions, always verify both the leap year status and the cumulative weekday shift before deciding that calendars match.

Final Answer:
The calendar for 2013 is the same as the calendar for 2002.