Kenneth Rosen Edition 6th Exercise 7.1 Question 6 (Page No. 471)

Question

Given below is a table where R is a relation having pairs (x,y) over the set of real numbers  and these ordered pairs will be in R if and only if the condition given on the left most side of the table is satisfied.

The various columns represent the various properties a relation can have

R-Reflexive

IR-Irreflexive

S-Symmetric

ATS-Anti-symmetric

AS-Asymmetric

T-Transitive.

Let me know if below table entries are correct.

Comments

Mistake : Relation with condition $xy = 0$ is Not Transitive. e.g. $(4,0)$ and $(0,4)$

Remaining are all correct entries.

---

Isn't x=+- y is antisymmetric? From the definition of antisymmetric if a,b belongs to R and b,a belongs to R then a=b.

---

@ghostman-No. For antisymmetry

$\forall x \forall y(((xRy)and(yRx))\rightarrow x=y))$ should hold

consider (2,-2) and (-2,2). Above implication is broken.Hence, not Anti-symmetric.

---

sir na bulao yr :(