If P = { x| x is a month of a year whose name begins with letter 'J' } and Q = { y | y is a month of a year having 30 days } , find
`P cup Q `

Answer

To solve the problem, we need to find the union of two sets, P and Q.

### Step-by-Step Solution:

1. **Identify Set P**:
- Set P consists of months of the year whose names begin with the letter 'J'.
- The months that meet this criterion are:
- January
- June
- July
- Therefore, we can write:
\[ P = \{ \text{January, June, July} \} \]

2. **Identify Set Q**:
- Set Q consists of months of the year that have 30 days.
- The months that have 30 days are:
- April
- June
- September
- November
- Therefore, we can write:
\[ Q = \{ \text{April, June, September, November} \} \]

3. **Find the Union of Sets P and Q**:
- The union of two sets, denoted as \( P \cup Q \), includes all unique elements from both sets.
- We combine the elements from both sets:
- From Set P: January, June, July
- From Set Q: April, June, September, November
- Now, we list all unique elements:
- January
- April
- June (common to both sets, listed once)
- July
- September
- November
- Therefore, we can write:
\[ P \cup Q = \{ \text{January, April, June, July, September, November} \} \]

### Final Answer:
\[ P \cup Q = \{ \text{January, April, June, July, September, November} \} \]