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While going through Relation I'm bit confuse on how to read the representation of empty relation. The ref. book I have, in that, it is represented following without proper parenthesis.

$R = \emptyset \subset A \times A $

It should be read as

$(R = \emptyset) \subset A \times A $

OR

$R = (\emptyset \subset A \times A) $

Sub Question: Which one is right representation?

$R = \emptyset \subset A \times A $ // Proper subset

OR

$ R = \emptyset \subseteq A \times A $ //Subset

Ubi.B
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  • There is nothing mysterious going on here, it's just the empty set. – CyclotomicField Jul 29 '20 at 02:00
  • @CyclotomicField I know that it is empty set. What I want to know is about symbolic representation. – Ubi.B Jul 29 '20 at 02:05
  • Notation is often entirely arbitrary and changes from author to author. As long as there is no confusion as to what you mean you're free to pick and choose what you prefer. – CyclotomicField Jul 29 '20 at 02:13
  • @CyclotomicField you are pointing which question? Main question or sub question? – Ubi.B Jul 29 '20 at 02:14
  • Don't overthink this - relations are first and foremost sets and the empty relation is the empty set. Changing the parenthesis in the first part is meaningless and the distinction in the sub question is arbitrary. – CyclotomicField Jul 29 '20 at 02:24

1 Answers1

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I'm not sure if this is what you're asking, but a "chain" of symbols like this $$R = \emptyset \subset A \times A$$ is normally interpreted as: $$R = \emptyset \mbox{ and } \emptyset \subset A \times A.$$

Just like $a \le b \le c$ is interpreted as $a \le b$ and $b \le c$.

Ted
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