Which of the following is **TRUE** about subsets of the real numbers?

Question

Accepted Answer

A. $\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}$

Each containment $\mathbb{N} \subset \mathbb{Z}$ (add zero and negatives), $\mathbb{Z} \subset \mathbb{Q}$ (each integer = $n/1$), $\mathbb{Q} \subset \mathbb{R}$ (rationals are real). The chain holds.
- **B** reverses the containments.
- **C** is false; $\sqrt{2} \in \mathbb{R}$ but $\sqrt{2} 
otin \mathbb{Q}$.
- **D** is false; $\mathbb{T}$ and $\mathbb{Q}$ are disjoint.

Answer

$\mathbb{Q} \subset \mathbb{Z} \subset \mathbb{N}$

Answer

$\mathbb{R} \subset \mathbb{Q}$

Answer

The set of irrational numbers $\mathbb{T}$ is a subset of $\mathbb{Q}$