: Composition and relation properties. For the following statements, provide a proof if the statement is true or give a counterexample if the statement is false. S and R are binary relations over the same domain. (b) If S is reflexive, then S∘S is reflexive. (c) If S and R are both anti-reflexive, then S∘R is anti-reflexive. (d) If S is anti-reflexive, then S∘S is anti-reflexive. (e) If S and R are both anti-symmetric, then S∘R is anti-symmetric. (f) If S is anti-symmetric, then S∘S is anti-symmetric.
: Composition and relation properties. For the following statements, provide a proof if the statement is true or give a counterexample if the statement is false. S and R are binary relations over the same domain. (b) If S is reflexive, then S∘S is reflexive. (c) If S and R are both anti-reflexive, then S∘R is anti-reflexive. (d) If S is anti-reflexive, then S∘S is anti-reflexive. (e) If S and R are both anti-symmetric, then S∘R is anti-symmetric. (f) If S is anti-symmetric, then S∘S is anti-symmetric.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Exercise 8.4.5: Composition and relation properties.
For the following statements, provide a proof if the statement is true or give a counterexample if the statement is false. S and R are binary relations over the same domain.
(b)
If S is reflexive, then S∘S is reflexive.
(c)
If S and R are both anti-reflexive, then S∘R is anti-reflexive.
(d)
If S is anti-reflexive, then S∘S is anti-reflexive.
(e)
If S and R are both anti-symmetric, then S∘R is anti-symmetric.
(f)
If S is anti-symmetric, then S∘S is anti-symmetric.
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