For r ∈𝐑^+, let Ar={x ∈𝐑:|x|

Question

For r ∈𝐑^+, let Ar={x ∈𝐑:|x|<r}. Determine ⋃r ∈𝐑^+ Ar and ⋂r ∈𝐑^+ Ar.

Accepted Answer

Step 1: Understand the definition of the set u005C( A_r u005C). The set u005C( A_r u003D u005C{ x u005Cin u005Cmathbf{R} : |

For $r \in \mathbf{R}^{+}$, let $A_r=\{x \in \mathbf{R}:|x|<r\}$. Determine $\bigcup_{r \in \mathbf{R}^{+}} A_r$ and $\bigcap_{r \in \mathbf{R}^{+}} A_r$.