Assume I have 4 sets: $A$, $B$, $C$, and $D$.

What is the mathematical notation to indicate that all of these sets are pairwise disjoint?

I can obviously type:

$$A \cap B = \emptyset$$ $$A \cap C = \emptyset$$


But I am looking for a more succinct and mathematically correct way of expressing this.

  • 6
    $\begingroup$ Usually people just say "pairwise disjoint". I don't know of any standard notation for this. $\endgroup$ – ChocolateAndCheese Mar 4 '17 at 0:45
  • 2
    $\begingroup$ You could just say "The sets are pairwise disjoint". Another way is if you have sets $A_1,A_2,...,A_n$, then you could write $A_i\cap A_j=\emptyset$ when $i\neq j$ for $i,j\in\{1,...,n\}$. $\endgroup$ – Dave Mar 4 '17 at 0:47
  • $\begingroup$ Also, if the sets are non-empty and you already have a symbol for their union, say $S=A \cup B \cup C \cup D$ then you can say that the sets form a partition of $S$ $\endgroup$ – fiftyeight Jul 22 '17 at 8:07
  • $\begingroup$ Both of the suggestions above are excellent, thank you. $\endgroup$ – Kostas Jul 23 '17 at 14:13

If you have indexed family $\{A_i\}_{i\in I}$, then you can write $A_i\cap A_j=\emptyset$, $i\neq j$. If not, I don't see any problem in just stating: "Let $A,B,C,D$ be pairwise disjoint." This will probably be more clear than any notation you could come up with, including my own suggestion.

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