1. The problem asks to write given sets in set builder notation. 2. Set builder notation describes a set by a property that its members satisfy. 3. For each set: a. The set is {7, 9, 11, 13, 15, 17}, which is consecutive odd numbers starting from 7 to 17. We can write it as: $$\{x \mid x = 7 + 2n, n \in \mathbb{Z}, 0 \leq n \leq 5\}$$ b. The set is {10, 20, 30, 40, …}, multiples of 10 starting from 10. Set builder notation: $$\{x \mid x = 10n, n \in \mathbb{N}\}$$ c. The set is {25, 50, 75, 100, 125, …}, multiples of 25 starting from 25. Set builder notation: $$\{x \mid x = 25n, n \in \mathbb{N}\}$$ d. The set is {January, February, … , December}, the months of the year. Set builder notation: $$\{x \mid x \text{ is a month of the year}\}$$ 4. Summary: a. $$\{x \mid x = 7 + 2n, n \in \mathbb{Z}, 0 \leq n \leq 5\}$$ b. $$\{x \mid x = 10n, n \in \mathbb{N}\}$$ c. $$\{x \mid x = 25n, n \in \mathbb{N}\}$$ d. $$\{x \mid x \text{ is a month of the year}\}$$