We are given two sets:

• Set P: $P = \{x \mid x \text{ is a multiple of 5 less than 30}\}$
• Set Q: $Q = \{x \mid x \text{ is an odd whole number}\}$

Step 1: List the elements of set $P$

Set $P$ consists of multiples of 5 that are less than 30. The multiples of 5 less than 30 are:

$P = \{ 5, 10, 15, 20, 25 \}$

Step 2: List the elements of set $Q$

Set $Q$ consists of all odd whole numbers. The odd whole numbers are:

$Q = \{ 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, \dots \}$

Step 3: Find the intersection of sets $P$ and $Q$

The intersection $P \cap Q$ consists of the elements that are in both sets $P$ and $Q$. From the elements listed above, the common numbers between $P$ and $Q$ are:

$P \cap Q = \{ 5, 15, 25 \}$

Final Answer:

$P \cap Q = \{ 5, 15, 25 \}$

Would you like more details or have any questions about this process?

Here are some related questions you might find interesting:

1. What is the union of sets $P$ and $Q$?
2. How would you define the complement of set $P$ in the universal set of natural numbers less than 30?
3. What is the difference between sets $P$ and $Q$?
4. If the universal set is the set of all whole numbers less than 30, what is the complement of $Q$?
5. How would you describe the relationship between the sets $P$ and $Q$ using set operations?

Tip: Always list the elements of each set clearly before performing operations like union, intersection, or difference. This helps avoid mistakes when comparing sets.