1. The problem asks for the meaning of the set \(\{(x,y) : x \in A, y \in B\}\). This is by definition the Cartesian product \(A \times B\), the set of all ordered pairs where the first element is from \(A\) and the second from \(B\). 2. Given \((3,5) \in \{(3,x), (3,8), (6,8)\}\), the pair must match the form \((3,x)\), so comparing coordinates, \(x = 5\). 3. If \(X = \{5\}\) and \(Y = \{3\}\), then \(n(X \times Y) = n(X) \cdot n(Y) = 1 \cdot 1 = 1\). 4. If \(X= \{2\}\), \(Y = \{1,3\}\), then \(n(X \times Y) = n(X) \cdot n(Y) = 1 \cdot 2 = 2\). 5. If \(X= \{2\}\), \(Y= \{0,4\}\), then \(n(X \times Y) = 1 \cdot 2 = 2\). 6. If \(n(X)=2\) and \(n(Y^2)=9\) (meaning \(n(Y)=3\) since \(Y^2\) is \(Y \times Y\)), then \(n(X \times Y) = n(X) \cdot n(Y) = 2 \cdot 3 = 6\). Final answers: 1. (b) \(A \times B\) 2. (c) 5 3. (d) 1 4. (d) 2 5. (d) 2 6. (a) 6