We have the following indirect implication of form equivalence classes:
| Implication | Reference |
|---|---|
| 359 \(\Rightarrow\) 20 | clear |
Here are the links and statements of the form equivalence classes referenced above:
| Howard-Rubin Number | Statement |
|---|---|
| 359: | If \(\{A_{x}: x\in S\}\) and \(\{B_{x}: x\in S\}\) are families of pairwise disjoint sets and \( |A_{x}| \le |B_{x}|\) for all \(x\in S\), then \(|\bigcup_{x\in S}A_{x}| \le |\bigcup_{x\in S} B_{x}|\). |
| 20: | If \(\{A_{x}: x \in S \}\) and \(\{B_{x}: x \in S\}\) are families of pairwise disjoint sets and \( |A_{x}| = |B_{x}|\) for all \(x\in S\), then \(|\bigcup_{x\in S}A_{x}| = |\bigcup_{x\in S} B_{x}|\). Moore [1982] (1.4.12 and 1.7.8). |
Comment: