• (10 pts) Prove that the relation S= {(x,y) E RR:x^2=y^2} is reflexive on R. symmetric and transitive.

Question

contestada

Respuesta :

AlonsoDehner AlonsoDehner · Answer 1 · 2019-09-11T03:51:38+02:00

Answer:

Step-by-step explanation:

Given that S is a relation in R such that

x,y is related if

[tex]x^2=y^2[/tex] for x,y real numbers

For any real number we have

[tex]x^2=x^2[/tex] hence S is reflexive

Similarly whenever

[tex]x^2=y^2[/tex] we get

[tex]y^2=x^2[/tex] Hence symmetric

When [tex]x^2=y^2 and\\y^2=z^2[/tex]

we get

[tex]x^2=z^2[/tex]

Thus transitive

Thus we find that S is reflexive, symmetric and transitive on R