Write the following sets in roster form and also in set builder form :
{months of a year having 31 days}

Answer

To solve the question of writing the set of months of a year having 31 days in both roster form and set builder form, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Months with 31 Days**:
- The months of the year are:
- January (31 days)
- February (28 or 29 days)
- March (31 days)
- April (30 days)
- May (31 days)
- June (30 days)
- July (31 days)
- August (31 days)
- September (30 days)
- October (31 days)
- November (30 days)
- December (31 days)
- From this, we can see that the months with 31 days are: January, March, May, July, August, October, and December.

2. **Write in Roster Form**:
- Roster form lists all the elements of the set explicitly.
- The set of months with 31 days in roster form is:
\[ \{ \text{January, March, May, July, August, October, December} \} \]

3. **Write in Set Builder Form**:
- Set builder form describes the properties of the elements in the set.
- We can express the set of months with 31 days as:
\[ \{ x \mid x \text{ is a month that has 31 days} \} \]

### Final Answer:
- **Roster Form**:
\[ \{ \text{January, March, May, July, August, October, December} \} \]
- **Set Builder Form**:
\[ \{ x \mid x \text{ is a month that has 31 days} \} \]