If A and B are two distinct sets, does that mean A and B are disjoint? Or if A is the subset of B, can A and B be two distinct sets? I am confused here that whether distint and disjoint sets mean the same? I have to find the intersection of two sets. It could be empty set if these two sets are disjoint. And it could be any other set if they are not.
So please help me understand the difference between distinct and disjoint sets if there is any.
Does distinct sets mean disjoint sets
elementary-set-theoryterminology
Best Answer
Two sets are equal if and only if they both have EXACTLY the same elements.
Two sets are disjoint if they do NOT have commons elements.
So no, to be DIFFERENT/DISTINCT is not the same that being DIsJOiNT.
$A=\{0,1\}$ and $B=\{0\}$ are DIFFERENTS (DISTINCT) ($1\in A$ but $1\notin B$), but they are not disjoint: $A\cap B=\{0\}$ (in fact, $B\subset A$).
Moreover, $A$ and $C=\{0,2\}$ are also differents (distinct), not disjoint $A\cap C=\{0\}$ and neither $C\subset A$ nor $A\subset C$.
$A$ and $D=\{2,3\}$ are differents (distinct) and disjoint.