1. **State the problem:** We need to list all elements in the set $B = \{x \in \mathbb{N} : x^3 \text{ is an odd number less than } 150\}$. This means we want natural numbers $x$ such that $x^3$ is odd and $x^3 < 150$. 2. **Recall important rules:** - A cube of a number $x$ is $x^3 = x \times x \times x$. - The cube of an odd number is always odd. - The cube of an even number is always even. 3. **Analyze the condition $x^3$ is odd:** Since $x^3$ is odd, $x$ itself must be odd. 4. **Find all odd natural numbers $x$ such that $x^3 < 150$:** Check odd numbers starting from 1: - $1^3 = 1$ (odd and less than 150) - $3^3 = 27$ (odd and less than 150) - $5^3 = 125$ (odd and less than 150) - $7^3 = 343$ (odd but greater than 150, so stop here) 5. **Conclusion:** The elements in $B$ are $\{1, 3, 5\}$. **Final answer:** $B = \{1, 3, 5\}$