Logic and sets · Binary relations · Power set · Empty set · Relation properties
A set \(A\) is given. Among its subsets a relation \(\sim\) is defined by
\[ X \subseteq A, \quad Y \subseteq A, \qquad X \sim Y \iff X \cap Y \neq \varnothing . \]
Determine whether \(\sim\) is reflexive, whether it is symmetric, whether it is antisymmetric and whether it is transitive.
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Serbian Regional Competition (Okruzno takmicenje) 1999, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source