This question involves calendar logic and understanding how the number of days in a month, especially February, affects the occurrence of weekdays. The core information is that a person was born on the fifth Monday of February in a particular year.

Understanding the Fifth Monday in February

For February to have a fifth Monday, two conditions must be met:

1. February must have 29 days. This implies that the year in question is a leap year.
2. The 1^st day of February must be a Monday.

Let's elaborate on the second point. If February 1^st is a Monday, then the Mondays in February would fall on the following dates:

• 1^st February (Monday)
• 8^th February (Monday)
• 15^th February (Monday)
• 22^nd February (Monday)
• 29^th February (Monday)

Only if February has 29 days (a leap year) and starts on a Monday can it have five Mondays. If February started on any other day (e.g., Tuesday), or if it had only 28 days, it would have a maximum of four Mondays.

Therefore, we can confidently conclude that in that particular year:

• February had 29 days (it was a leap year).
• The 1^st February was a Monday.

Analyzing Each Calendar Statement

Now, let's examine each given statement based on our deduction that February 1^st was a Monday and it was a 29-day month:

Statement 1: The 2^nd February of that year is a Tuesday

Since we have established that the 1^st February of that year was a Monday, the day immediately following, which is the 2^nd February, would naturally be a Tuesday.

Therefore, this statement is correct.

Statement 2: There will be five Sundays in the month of February in that year

If the 1^st February is a Monday, we can list the days of the week for the first few days to find the Sundays:

• February 1: Monday
• February 2: Tuesday
• February 3: Wednesday
• February 4: Thursday
• February 5: Friday
• February 6: Saturday
• February 7: Sunday

The Sundays in February would then fall on the 7^th, 14^th, 21^st, and 28^th. Even though February has 29 days (it's a leap year), the 29^th would be a Monday (since 29 days means the 29th day falls on the same day as the 1st if we consider $29 \text{ days} = 4 \times 7 \text{ days} + 1 \text{ day}$, so the 29th is 1 day after the 4th full week, making it a Monday if the 1st was a Monday). This means there are only four Sundays in that February.

Therefore, this statement is incorrect.

Statement 3: The 1^st February of that year is a Sunday

Our initial deduction for February to have a fifth Monday required that the 1^st February must be a Monday. This statement directly contradicts our finding.

Therefore, this statement is incorrect.

Statement 4: All Mondays of February in that year have even dates

We identified the Mondays in February as the 1^st, 8^th, 15^th, 22^nd, and 29^th.

Upon reviewing these dates, the 1^st, 15^th, and 29^th are odd dates. Consequently, not all Mondays have even dates.

Therefore, this statement is incorrect.

Conclusion on Calendar Deduction

Based on the detailed analysis, only the statement that the 2^nd February of that year is a Tuesday is consistent with the condition that February had a fifth Monday.