2.7 Partial Orders and Equivalence | 2.7 Partial Orders and Equivalence | Unit 2: Structures | Mathematics for Computer Science | Electrical Engineering and Computer Science

Properties Of Relations

Let \(R\) and \(S\) be relations on the set \(A\). Which of the following statements about \(R\) and \(S\) are true?

If \(R\) is reflexive, then the complement of \(R\) is also reflexive.

If \(R\) is symmetric, then the complement of \(R\) is symmetric.

If both \(R\) and \(S\) are reflexive, then \(R\cap S\) is also reflexive.

While \(\leq\) is reflexive, its complement \(>\) is not.