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 cap Q `

Answer

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

### Step 1: Define Set P
Set P is defined as the set of months of the year whose names begin with the letter 'J'.
- The months that start with 'J' are:
- January
- June
- July

So, we can write:
\[ P = \{ \text{January, June, July} \} \]

### Step 2: Define Set Q
Set Q is defined as the set of months of the year that have 30 days.
- The months that have 30 days are:
- April
- June
- September
- November

So, we can write:
\[ Q = \{ \text{April, June, September, November} \} \]

### Step 3: Find the Intersection of P and Q
The intersection of two sets, denoted as \( P \cap Q \), is the set of elements that are common to both sets.
- From set P, we have: January, June, July
- From set Q, we have: April, June, September, November

Now, we look for common elements:
- The only month that appears in both sets is June.

Thus, we can write:
\[ P \cap Q = \{ \text{June} \} \]

### Final Answer
The intersection of sets P and Q is:
\[ P \cap Q = \{ \text{June} \} \]

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