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
