Final Answer:
No, the relation between the months of the year and the possible number of days per month is not a function. This is because some months have more than one possible number of days, violating the definition of a function where each input (month) must correspond to a unique output (number of days).
Step-by-step explanation:
In a function, each input (in this case, each month) must have a unique output (number of days). However, in the case of the mapping between the months of the year and the possible number of days per month, there are exceptions. For example, February can have 28 or 29 days in a leap year. This violation of the one-to-one correspondence between inputs and outputs means the relation does not satisfy the definition of a function.
To further clarify, let's consider January. For any given year, January consistently has 31 days. However, for February, there is variability – it can be either 28 or 29 days. This means that for the same input (February), there are multiple possible outputs (28 and 29). As this violates the fundamental property of a function, where each input must have a unique output, the relation between months and days is not a function.
In conclusion, the relation between months and the possible number of days does not meet the criteria of a function due to the variability in the number of days for certain months. Functions require a clear and unique mapping from each input to an output, and the exceptions in the days of February make the relation non-functional.