For the following statement S and proposed proof, either (1) S is true and the proof is
Chapter 8, Problem 8.73(choose chapter or problem)
For the following statement S and proposed proof, either (1) S is true and the proof is correct, (2) S is trueand the proof is incorrect or (3) S is false (and the proof is incorrect). Explain which of these occurs.S: Every symmetric and transitive relation on a nonempty set is an equivalence relation.Proof Let R be a symmetric and transitive relation defined on a nonempty set A. We need only show thatR is reflexive. Let x A. We show that xRx. Let y A such that xRy. Since R is symmetric, yRx.Now xRy and yRx. Since R is transitive, xRx. Thus R is reflexive.
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