Is this correct? If it is, is there a better way to write it?
$C\cap B≠\{Ø\}$
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9It should be $C \cap B \neq\emptyset$ (empty set) instead of $C \cap B \neq {\emptyset}$ (a set containing one element which happens to be an empty set) – Sil Apr 21 '22 at 06:14
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2There are also other (worse?) ways to write it, e.g. $(\exists x)(x\in C\land x\in B)$ – Apr 21 '22 at 06:43
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1One more: $\mathcal{P}(C\cap B)\geq 1$. – Ivan Kaznacheyeu Apr 21 '22 at 06:46
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2@IvanKaznacheyeu But does not $\mathcal P$ denote the power set? I've never seen it used to mean the cardinality. I'd write it as $|C \cap B| \ge 1$. – Prime Mover Apr 21 '22 at 09:40
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1@KaviRamaMurthy No, it is wrong. – Prime Mover Apr 21 '22 at 09:40
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1@PrimeMover, you're correct. I've should use other designation. – Ivan Kaznacheyeu Apr 21 '22 at 09:44
1 Answers
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Some suggestions
- $B$ and $C$ have at least one element in common
- There is at least one element that belongs to both $B$ and $C$
- $B$ and $C$ are not disjoint
- $B \cap C$ is non-empty
- $B \cap C \ne \emptyset$
- $\exists x$ such that $ x \in B \cap C$
They all say the same thing. Picking one is really just a matter of taste and style.
bubba
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