Chapter II, Problem 3E

True or false. When the answer is false, explain your reasoning.

1. 0 is a natural number.
2. $\left(5+2i\right)\left(5-2i\right)$ is a real number.
3. $\mathbb{Z}\subseteq \mathbb{Q}.$
4. $\mathbb{Q}\subseteq \mathbb{Z}.$
5. $\left[2,5\right]=\left\{2,3,4,5\right\}.$
6. $\left[3.2,4.7\right]\subseteq \left(3.2,4.7\right).$
7. $\left(6,9\right)\subseteq \left[6,10\right).$
8. $\left(3.2,4.7\right)\subseteq \left[3.2,4.7\right].$
9. $\left[7,10\right]\subseteq ℝ.$
10. $\left[7,10\right]\subseteq \left\{7,8,9,10\right\}.$
11. $\left[0.5,1.5\right]\subseteq \mathbb{Q}.$
12. $\left(-8,5\right)\subseteq \left(-2,6\right).$
13. There are exactly three prime numbers between 40 and 50.