So reflexive is equal to each other. Like x R x.
Symmetric is x R y = y R x
Transitive is if x R y and y R z, then x R z.
The relation is symmetric because if A \cap C = B \cap C, then C \cap A = C \cap B. Is this correct?
The relation is also transitive, because if A \cap C and B \cap C...
Let U be a universal set, and let C be any subset of U. Let R be the relation on P(U) defined by A R B if $A \cap C = B \cap C$. Determine whether the relation is reflexive, symmetric, and/or transitive. Prove you answer.