1.2 For each set, give TWO elements belonging to the set (a) \( A_{3}=\left\{\frac{2 n^{2}-n-10}{2 n^{2}+3 n-2} \quad n \in \mathbb{Z}\right\} \) (b) \( A_{4}=\{x \in \mathbb{Q} \quad x \in(0,6]\} \)

For the set \( A_{3} \), let's take \( n = 0 \) and \( n = 1 \). - When \( n = 0 \): \[ \frac{2(0)^2 - (0) - 10}{2(0)^2 + 3(0) - 2} = \frac{-10}{-2} = 5 \] - When \( n = 1 \): \[ \frac{2(1)^2 - (1) - 10}{2(1)^2 + 3(1) - 2} = \frac{2 - 1 - 10}{2 + 3 - 2} = \frac{-9}{3} = -3 \] So, two elements of \( A_{3} \) are \( 5 \) and \( -3 \). For the set \( A_{4} \), we can select \( x = 1 \) and \( x = 5 \). - The number \( 1 \) is rational and clearly falls within the range \( (0,6] \). - The number \( 5 \) is also rational and lies in the same range. Thus, two elements of \( A_{4} \) are \( 1 \) and \( 5 \).