IV. Give the roster form of the following: 1. \( \{x / \mathrm{x} \) is a counting number, \( 25 \leq \mathrm{x} \leq 30\} \) 2. \( \{2 \mathrm{x} / \mathrm{x} \in \mathrm{z}+, \mathrm{x}>1\} \) 3. \( \left\{\mathrm{x} / \mathrm{x} \in \mathrm{N}, \mathrm{x}>\mathrm{x}^{2}\right\} \)

To express the given sets in roster form, we will identify the elements that satisfy the conditions specified in each set. 1. For the set \( \{x / \mathrm{x} \) is a counting number, \( 25 \leq \mathrm{x} \leq 30\} \): - The counting numbers between 25 and 30 (inclusive) are: 25, 26, 27, 28, 29, and 30. - Therefore, the roster form is: \[ \{25, 26, 27, 28, 29, 30\} \] 2. For the set \( \{2 \mathrm{x} / \mathrm{x} \in \mathrm{z}^+, \mathrm{x}>1\} \): - Here, \( \mathrm{z}^+ \) refers to the set of positive integers (counting numbers). The condition \( \mathrm{x} > 1 \) means \( \mathrm{x} \) can take values 2, 3, 4, and so on. - The corresponding values of \( 2\mathrm{x} \) for \( \mathrm{x} = 2, 3, 4, \ldots \) are: 4, 6, 8, 10, 12, ... - Thus, the roster form is: \[ \{4, 6, 8, 10, 12, \ldots\} \] (This set continues indefinitely with even numbers greater than or equal to 4.) 3. For the set \( \left\{\mathrm{x} / \mathrm{x} \in \mathrm{N}, \mathrm{x}>\mathrm{x}^{2}\right\} \): - The natural numbers \( \mathrm{N} \) are 1, 2, 3, 4, ... The condition \( \mathrm{x} > \mathrm{x}^{2} \) implies \( \mathrm{x} \) must be less than 1, since for any natural number \( \mathrm{x} \geq 1 \), \( \mathrm{x}^{2} \) will always be greater than or equal to \( \mathrm{x} \). - Since there are no natural numbers less than 1, this set is empty. - Therefore, the roster form is: \[ \emptyset \] In summary, the roster forms are: 1. \( \{25, 26, 27, 28, 29, 30\} \) 2. \( \{4, 6, 8, 10, 12, \ldots\} \) 3. \( \emptyset \)