Given sets A = 2, 3, 4, 5, 6, 7, 8, 9 and B = 2, 3, 5, 7. Find the intersection of A and B and draw a Venn diagram. Also, consider sets P and Q...

The elements that are present in both set A and set B are 2, 3, 5, and 7.

$$A \cap B = \boxed{\{2, 3, 5, 7\}}$$

Since all elements of B are also in A, set B is a subset of set A. This means the circle representing B should be drawn entirely inside the circle representing A.

• Place the elements common to both A and B (which are all elements of B) inside the inner circle (B): $\{2, 3, 5, 7\}$.
• Place the elements that are in A but not in B in the region of circle A outside circle B: $\{4, 6, 8, 9\}$.

Here is the Venn diagram:

\begin{tikzpicture} \begin{scope} \draw (0,0) circle (2cm) node[above right] {$A$}; \draw (0,0) circle (1cm) node[above right] {$B$}; \node at (0, 0.5) {2}; \node at (-0.5, 0) {3}; \node at (0.5, 0) {5}; \node at (0, -0.5) {7}; \node at (1.5, 1.5) {4}; \node at (-1.5, 1.5) {6}; \node at (1.5, -1.5) {8}; \node at (-1.5, -1.5) {9}; \end{scope} \end{tikzpicture}

Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. The prime numbers less than 10 are 2, 3, 5, and 7.

$$P = \boxed{\{2, 3, 5, 7\}}$$

Even numbers are integers divisible by 2. The even numbers less than 10 are 0, 2, 4, 6, and 8.

$$Q = \boxed{\{0, 2, 4, 6, 8\}}$$